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TEXTILE CALCULATIONS 



INSTRUCTION PAPER 



PREPARKD BY 

Fenwick Umpleby 

Yorkshire College, England 

City and Guilds of London Institute 

Head of Department of Textile Design 

Lowell Textile School 



AMERICAN SCHOOL, OF CORRE^SPONDENCE 



CHICAGO ILLINOIS 

U.S.A. 



^ 



LIBRARY of CONGRESS 
Two eooies Recetved 

APR 23 1906 

^ CopyrliEht Entry 
CLASS <^ XXc No, 
COPY B. ' 



Copyright 1906 by 
American School of Co:xrespondence 



Entered at Stationers' Hall, I^ondon 
All Rig-hts Reserved 



'?-27 9o^ 



TEXTILE CALCULATIONS, 

SIZES OF YARNS — NUMBERING. 

The sizes of yarns are designated by the terms cut^ run^ hank^ 
county skein, dram, grain, etc., all of which are based upon two 
elementary principles, i.e., weight and length. Each term repre- 
sents a certain length of yarn for a fixed weight, or vice versa; 
but unfortunately there are different standards of weights and 
measures, which results in a great deal of confusion. The largest 
variety of terms is found in the woolen industry. In the United 
States we have woolen cut, run, grain, etc., when all may be 
reduced to a common basis. There is no doubt that the adoption 
of an international standard would benefit the textile industry, 
but which standard to adopt is a question on which manufacturers 
disagree. 

A simple method would be 1,000 metres as the unit of length, 
to be called count or number, and the number of units which weigh 
one kilogram to represent the counts or number of yarn. By this 
method the counts of the yarn would always show at a glance the 
number of metres per gram, as 

No. 1 — 1,000 metres = 1 kg. 

No. 2— 2,000 metres = 1 kg. 

No. 2%— 2,500 metres = 1 kg. 
WOOLEN COUNTS. 
The simplest method in use at present is the one used in the 
New England States, in which IN'o. 1 woolen yarn represents 100 
yards to the ounce, or 1,600 yards to the pound, as a standard. 
The number of the yarn is the number of yards contained in one 
ounce, divided by 100. The yarn is spoken of as so many hundred 
yards to the ounce. Thus, 

No. 4 = 400 yards to 1 ounce. 
No. 4% = 450 yards to 1 ounce. 
No. 5 = 500 yards to 1 ounce. 
No. 53^ = 512.5 yards to 1 ounce. 

A comparison of Troy and Avoirdupois weights may be made 

by the following tables. The Avoirdupois table should be com- 



TEXTILE CALCULATIONS 



iiiitted to iiieiiiury, as it is used very extensively in Textile 
Calculations. 

AVOIRDUPOIS WEIGHT. 
437.5 grains (gr.) = 1 ounce (oz.) 

16 drams (dr.) = 1 ounce. 

7,000 grains = 1 pound (lb.) 

16 ounces = 1 pound. 

100 pounds = 1 hundredweight (cwt.) 

20 hundredweight = 1 ton (t.) 
Note. — 25 pounds are sometimes called a quarter. 

TROY WEIGHT. 

24 grains (gr.) = 1 pennyweight (pwt.) 
20 pennyweights = 1 oance (oz.) 
5,760 grains = 1 pound (lb.) 

12 ounces = 1 pound. 

It is necessary to familiarize one's self with the standard num- 
bers of the various yarns; also, as in the case of woolen yarns, 
where different standard numbers are used for the various terms, 
it is well to be familiar with the standard number of each term, 
as by this means a great deal of confusion will be avoided. 

TABLE OF RELATIVE COUNTS OF YARN. 



Yarn. 


Size. 


Stand 


Woolen 


No. 1 run = 


1,600 


u 


No. 1 cut = 


800 


u 


No. 1 skein = 


256 


Worsted 


No. 1 count = 


560 


Cotton 


No. 1 count = 


840 


Linen 


No. 1 lea = 


300 


Spun silk 


No. 1 count = 


840 



Such fibres as linen, jute, hemp and ramie fibre are usually 
figured by the lea of 300 yards to the pound. In the grain system 
the w^eight in grains of 20 yards designates the counts. Thus, if 20 
yards weigh 20, 25, or 30 grains the counts would be No. 20, No. 
25 or No. 30 grain yarn respectively. 

SILK COUNTS. 

Spun Silk is based upon the same system as cotton, i.e., 
hank of 840 yards, and the number of such hanks w^hich weigh 
one pound denotes the counts. 

Note. — Silk that has been re-manufactured or re-spun is called spun 
silk. 



TEXTILE CALCULATIONS 



Dram Silk. The system adopted in the United States for 
specifying the size of silk is based on the weight in drams of 
a skein containing 1,000 yards. Thus a skein which weighs 5 
drams is technically called 5-dram silk. The number of yards 
of 1-dram silk in a pound must accordingly be 16x16x1,000 
or 256,000. 

Note. — 1,000 is multiplied by (16x16) because there are 16 drams in 
one ounce and 16 ounces in one pound. 

Tram Silk is based on a system in which 20,000 yards per 
ounce is used as a standard. 

WORSTED COUNTS. 

This system is based upon the hank of 560 yards, the counts 

being determined by the number of such hanks contained in one 

pound of yarn. 

No. 1 = 560 yards in 1 pound. 
No. 2 = 1,120 yards in 1 pound. 
No. 3 = 1,680 yards in 1 pound. 

COTTON COUNTS. 

Cotton is based upon the hank of 840 yards, and the number 
of such hanks which weigh one pound denotes the -counts. The 
following tables are used when calculating cotton yarns: 

IX yards = the circumference of reel, or 1 wrap. 
120 yards=: 1 lea or 80 wraps of the reel. 
840 yards = 7 leas or 1 hank. 

No. 1 cotton = 840 yards in 1 pound. 
No. 2 cotton = 1,680 yaTds in 1 pound. 
No. 3 cotton = 2,520 yards in 1 pound. 

Linen and Similar Fibres such as jute^ hemp^ ra.m^ie fihre^ 

and China grass are numbered by using as a base the lea of 300 

yards; the number of such leas which weigh one pound being 

the counts. 

No. 1 = 300 yards in 1 pound. 
No. 2 = 600 yards in 1 pound. 
No. 3 = 900 yards in 1 pound. 

English Woolen or Skein System — This system is based 
upon the skein of 256 yards, the number of such skeins which 
weigh one pound being the counts. In England the yarn is spoken 
of as so many yards to the dram, or so many skeins, which is the 



TEXTILE CALCULATIONS 



same thing when referring to its size. Thus 6 skeins or 6 yards 
to the dram; 10 skeins or 10 yards to the dram. 

No. 1 = 256 yards to the pound. 
No. 2 = 512 yards to the pound. 
No. 3 = 768 yards to the pound. 

The standard weight is one dram, and the number of yards to 
that weight is regulated according to requirements. 

The Philadelphia or Cut System is based upon the cut of 
300 yards, the number of such hanks which weigh one pound 
denoting the counts. 

No. 1 = 300 yards to the pound. 
No. 2 = 600yards to the pound. 
No. 3 = 900 yards to the pound. 

Rule 1. To find the yards per pound of any given counts of 
woolen run, woolen cut, worsted, cotton, linen, and spun silk. 
Multiply the standard number by the given counts. 

Example. How many yards per pound in No. 15 cotton, 3 
run woolen, No. 20 worsted 'i No. 15 cotton, 840x15 = 12,600 
yards. 3 run woolen, 1,600x3 = 4,800 yards. No. 20 worsted, 
560x20 = 11,200 yards. 

Rule 2. To find the weight of any number of yards of a 
given counts, the number of yards being given. Divide the given 
number of yards by the counts X the standard number. 

Example. What is the weight of 107,520 yards of No. 32 
cotton ? 

107,520 ^ (32 X 840) -= 4 pounds. 

Find the weight of 12,400 yards of 30's worsted, 11,960 
yards of 20 lea linen, and 7,200 yards of 4J run woolen. 

Rule 3. It is often necessary to know the weight in ounces 
of a small number of yards. Multiply the given number of yards 
by 16, and divide by the counts X the standard number. 

Example. "What is the weight in ounces of 2,800 yards of 
No. 20 worsted ? 

(2,800x16) ^ (20X560) = 4 ozs. 

The woolen -run system is the most simple of all textile yarn 
calculations, as 100 yards per ounce -= No. 1 run. 



TEXTILE CALCULATIONS 



Rule 4. To find the weight in ounces of a given number of 
woolen-run yarn. Add two ciphers to the counts and divide into 
the given number of yards. 

Example. What is the weight of 2,700 yards of 2-run 
woolen ? 

2,700 ^ 200 = 13.5 ozs. 

Rule 5. Grain System. To find the counts of a woolen 

!i -'^ad, the number of yards and weight being known. (The 

Weight in grains which 20 yards weigh designates the counts.) 

Multiply the given weight by grains in 1 lb. and by 20 yards, and 

divide by the given number of yards of yarn. 

Example. What is the counts of 28,000 yards which weigh 
4 pounds ? 

4X7,000X20 „..„., 

28,000 = 20 grams per 20 yards. 

' ^0 s counts. Ans. 

EXAMPLES FOR PRACTICE. 

1. How many yards of yarn in 1 lb. of each of the following 
numbers: No. 23 cotton. No. 5 run woolen. No. 32 worsted. No. 
22 lea linen. No. 25 spun silk ? 

2. Obtain the counts of the following yarns: 12,600 yards 
cotton = lib.; 11,200 yards worsted = 1 lb.; 12,000 yards 
linen = 1 lb.; 13,440 yards spun silk = 1 lb. 

3. How many yards per pound in 4 dram silk, 5 dram silk, 
and 3 dram silk ? 

4. Woolen grain system. How many yards per pound in 7 
grain woolen, and 5 grain woolen ? 

5. If 16,800 yards of yarn weigh 1 pound, what counts 
would represent this length and weight in worsted, cotton, and 
woolen ? 

6. The weight of 1,680 yards of worsted is 3 ounces. What 
is the counts? 

7. Find the respective weights of 800 yards, 4,200 yards, 
and 6,300 yards of [a) 4-run woolen, (^b) No. 30 worsted, (c) No. 
30 cotton. 

8. What is the weight of 4,200 yards of 30's cotton; 3,600 
yards of 32's worsted; 1,850 yards of 2 J woolen ? 



TEXTILE CALCULATIONS 



9. AVhat is the weight of 1,840 yards of 3_^ run woolen 
yarn, 2,100 yards of 4| run, 3,040 yards of SI run ? 

10. Find the cotton counts of these yarns: 14,000 yards 
weigh 3A pounds; 37,620 yards weigh 4J^ pounds; 29,640 yards 
weigh 4 pounds. 

Note. — The terms count, 'counts, number, numbers, etc., are used 
wlieu speakinj^ of the size of yarn. They are written in various ways, 
for instance. No. 1 counts, I's, No. I's, and No. 1. All represent the 
same thing. 

METRIC MEASUREMENTS AND WEIGHTS. 

Linear Measure. 

1 millimeter (mm.) 

10 millimeters = 1 centimeter (cm.) 

10 centimeters = 1 decimeter (dm.) 

10 decimeters = 1 meter (m.) 
10 meters = 1 decameter (decam.) 

10 decameters = 1 hectometer (hm.) 

10 hectometers = 1 kilometer (km.) 
Measures of Weight. 

1 milligram (mg.) 

10 milligrams = 1 centigram ( eg. ) 

10 centigrams = 1 decigram (dg.) 

10 decigrams = 1 gram (g.) 
10 grams = 1 decagram (decag.) 

10 decagrams = 1 hectogram (hg.) 

10 hecograms = 1 kilogram (kg.) 

The Continental method for worsted is based upon 1,000 
metres per kilogram, e.g., No. 1 counts contains 1,000x1 metre. 
No. 2 counts contains 1,000 X 2 metres. No. 3 counts contains 
1,000x3 metres, etc. 

TABLE OF EQUIVALENTS. 
= 3.937 inches. 

15.4999 inches. 
28.35 grams. 
= 437.5 grains. 
= 15.432 grains. 

: 2.2046 pounds or 15432.2 grains. 

1.094 yards. 
39.37 inches. 
- 1 kg. or 2.2046 pounds worsted yarn. 

1,000 m. = 1,094 yards. 

In the metric system, woolen counts are based on the same 
principle as w^orsted counts, that is, 1,000 metres of No. 1 woolen 



1dm. 


1dm. 


1 oz. 


1 oz. 


1 gram 


1kg. 


Im. 


Im. 


1,000 m. 



TEXTILE CALCULATIONS 



weigh 1 kg. or 1,000 grams. This also applies to cotton, linen, 
silk, jute, etc. 

It will be seen from this that the metric system possesses a 
great advantage over the many varied systems now in use, inas- 
much that it is simpler in calculations, decimals doing away with 
the more complicated fractions of the English system (such as |-, 
±^^ 2T_^ 39^ etc.), and the uniformity of difference between kilo- 
grams, hectograms, decagrams, etc., is simpler than the complex 
system of tons, hundred -weights, pounds, ounces, drams, and 
grains. 

To reduce kilograms to grams, it is only necessary to multiply 
the given number by 1,000, while to reduce from pounds to drams 
in English the given number must be multiplied by 16 X 16. With 
metric numbers the difference may be easily computed. Taking 
2.25 kg. of yarn and wishing to find the weight in grams, the 
following simple process is all that is required: 
2.25X1,000 = 2,250 grams. 

This weight represents approximately 4 pounds 8 ounces, and 
wishing to find the weight in drams the following complicated 
equation is necessary: 

4iXl6x 16 = drams. 

Another advantage of the metric system is that while a No. 
1 in the English system equals 1,600 yards woolen, 560 yards 
worsted, 840 yards cotton, 300 yards linen, etc., to the pound, in 
the metric system a N'o. 1 count has 1,000 metres to the kilogram 
in every variety of yarn, which gives a simple basis of comparison 
between the yarns. 

THROWN SILK. 

The Continental Europe system of numbering thrown silk is 
based upon the hank of 400 French ells. The skein or hank is 
476 metres, or 520 yards, and the weight of this hank in deniers 
denotes the counts. 

533.33 deniers equal 1 ounce. 

If 1 hank of the above length weighs 10 deniers, the counts 
equal No. 10 denier. 

Approximately No. 1 denier = 533^X520 = 277,333 yards 
per ounce. 



10 TEXTILE CALCULATIONS 

No. 40 denier = (533% x 520) --40 = 6,933% yards per ounce. 
No. 60 denier = (533% x 520 )h- 60 =4,622% yanis per ounce. 

CHANGING THE COUNTS OF YARNS, 

The three great fibres, wool, worsted, and cotton, are mixed 
to a large extent. There are goods composed of woolen filling and 
cotton warp, worsted filling and cotton warp, woolen and worsted 
filling combined with cotton warp, and also woolen and worsted 
warps combined with cotton and woolen fillings; so it is important 
rliat the calculations pertaining to each should be thoroughly under- 
stood. The calculations in this work are directed towards these 
requirements. There are shorter methods of calculation which 
may be used by those fully conversant with the various particulars 
concerning textile manufactures, but it matters little which system 
is used if it is simple and reliable. 

Changing the Counts of one System of Yarn into the Equiv= 
alent Counts of Another System of Yarn. 

Rule 6. To change cotton counts into woolen runs. Multi- 
ply 840 by the known cotton counts and divide by 1,600, the 
standard yards per pound of No. 1 run woolen. 

Example. What is the size of a woolen thread equivalent to 
a 20's cotton ? 

(20X840)-^ 1,600= lOi run woolen. 

Rule 7. To chancre cotton counts into worsted counts. Mul- 
tiply 840 by the known cotton counts, and divide by 560, the stand- 
ard yards per pound of No. 1 worsted counts. 

Example. What is the equivalent in a worsted thread to a 
30's cotton ? 

(30x840)-^560 = 45's worsted. 

Rule 8. To change woolen runs into worsted counts. Mul- 
tiply 1,600 by the known woolen runs, and divide by 560, the 
standard yards per pound of No.' 1 worsted counts. 

Example. What is the equivalent in a worsted thread to a 
7 run woolen ? 

(7 X 1,600) -- 560 = 20's worsted. 

Rule 9. To change woolen runs, worsted counts, and cotton 
counts into their equivalents in linen or Philadelphia cuts. 
Multiply by the woolen, worsted, or cotton standard, and divide 



TEXTILE CALCULATIONS 11 

by 300, the standard number of yards which equals 1 lea linen 
and 1 cut woolen. 

Example. What are the equivalents in linen counts to a 
' 8 run woolen, 20's worsted, and 24's cotton ? 

(3X1,600) -^300 = 16 lea linen. 

Rule lo. To change woolen, worsted, linen, or cotton counts 
to their equivalents in the grain system. Multiply 7,000 grains 
by 20 (the yards representing the grain standard) and divide by 
the standard of the other yarn. 

Example. What is the equivalent in the grain system to a 
20's cotton ? 

7,000x20 

20X840 ^ ^'^^ "^^^^^'- 
What is the equivalent in the grain system of the following 
yarns, 24's worsted, 4 run woolen, 16 lea linen ? 

Rule II. To change woolen, worsted, linen, or cotton counts 
to their equivalents in the dram system. Multiply the given 
weight by drams per pound and by the yards in one dram, then 
divide by the given length of yarn. 

Example. What is the equivalent in the dram system to a 
ISTo. 30 cotton ? 

1X256X1,000 _^ 
30X840 - -^^•-^^• 

Find the equivalent in the dram system to 24's cotton, 4 J 
run woolen, 30's worsted. 

Rule 12. To change woolen, worsted, linen, and cotton counts 
to their equivalents in the denier system. Multiply the yards in 
one hank (520), deniers in one ounce (533^), and ounces in 1 
pound (16) together and divide the product by the length of 1 
pound of yarn of the known counts. 

Example. What is the equivalent in the denier system to a 
30's worsted ? 



520X5331X16 

' 30X56 = ^^^--'^ ^"^^"^' y^^'^- 



Rule i3. To change metric counts to English counts. The 
number of metres in one kilogram (1,000) multiplied by the 



12 TEXTILE CALCULATIONS 

inmiber of inches in one metre (39.37) will give the total num- 
ber of inches. This divided by the inches in one yard (36) will 
give the total number of yards, and again divided by the weight 
of 1 km. X the standard number will give the English counts, 
or constant. 
Solution: 

1,000x39.37 



36x560x2.205 
1,000X39.87 



.885 worsted count. 

.590 cotton and spun silk constant. 



36X840X2.£05 

36xl%fxl205 = •^^^^' '^y •^^' '^^^^^" constant. 
1,000x39.37 



36X300X2.205 



1.653 linen and woolen cut constant. 



1,094 - 


2 


496.1- 


- 560 


496.1- 


- 840 


496.1- 


-1,600 


496.1- 


- 300 



The English .885 is equal to a No. 1 metric worsted. 
" *' .590*' " ""No. 1 " cotton or spun silk. 

u a ^iQ u u ,i u ^Q I u woolen. 

" " 1.653 '« " " ''No. 1 " linen, etc. 

Proof 

1 metre = 1.094 yards. 1 kilogram = 2.205 pounds. 
1,000 metres No. 1 = 1 kilogram = 2.205 pounds. 
1,000 metres = 1,094 yards. 

2.205 = 496.1 yards per pound. 

= .885 worsted constant. 

.590 cotton " 

= .310 woolen *'^ 

1.653 linen "' 

Rule b4. The English count divided by the constant will 
give the metric count. 

Example. English 20's cotton -f-. 590 = 33. 89 metric cotton 
counts. 

Find the metric counts of 24:'s worsted, 6 run woolen, and 18 
lea linen. 

Rule 15. The metric count multiplied by the constant will 
give the English count. 

.310x20 metric woolen = 6.2 run woolen. 

Find the counts in English of the following metric counts: 
23.6 cotton, 28.2 worsted, and 16 woolen. 

TWISTED, PLY, AND COflPOUND YARNS. 

Yarns spun from different fibers are frequently twisted 
together for decorative purposes, and also for strength, e.(/., silk 



TEXTILE CALCULATIONS 1^ 



to cotton, worsted to woolen, etc. As yarns may be spun in one 
place and consigned for use in localities where different sys- 
tems of numbering yarns are in use, it is necessary to change 
any given number into the equivalent count of some other 
denomination. 

Worsted and cotton yarns are usually numbered according to 
the count of the single yarn, with the number of ply, threads, or 
folds, placed at the left, or before it. Thus 2-40's cotton 
yarn indicates that the yarn is composed of two threads of 4:0's 
single, making a two-fold or two-ply yarn of 20 hanks to the 
pound, and must be considered as representing 20 times 840 
yards; but when written 40's or 1-40's it represents 40 hanks or 
40 times 840 yards to the pound. 

Sjnin silk yarns are generally two or more ply, and the num- 
ber of the yarn always indicates the number of hanks 'in one 
pound. The number of ply is usually written after the hanks per 
pound. Thus 60-2 or 60's-2 spun silk indicates that the yarn is 
60 hanks to the pound composed of two threads of other 
counts. 

TiDO-ply woolen yarns are usually designated " Double and 
Twist" yarns, thus, 6 run black and white " D & T" would mean 
that one black thread of 6 run and one white thread of 6 run have 
been doubled and twisted, and represent a thread which is equiva- 
lent to a 3 run minus the take-up. 

When two or more single threads are twisted together, the 
result is a heavier yarn. It is necessary then to find the number 
of hanks or skeins per pound of the combined thread, but it must 
be understood that two threads, 20 yards long, twisted together 
will be much shorter than the orig^inal two threads. This can be 
proved by twisting together two threads of a given length, w^eigh- 
ing them, and again measuring the twisted thread, or by obtaining 
two threads of the original yarn of the exact length of the twisted 
yarn and comparing their weights. This process is known as 
finding the equivalent or resultant counts. 

Ply yarns composed of threads of equal counts. The new 
count is found by dividing the given counts by the number of ply 
or threads twisted together, 2-ply 60's = No. 30, written 2-60's ; 



14 TEXTILE CALCULATIONS 

8-ply GO'S = No. 20, written 3-60'8 ; 4-ply GO's = No. 15, 
written 4-r)0's. 

Assuming there is no variation in the take-up of each yarn 
during twisting, equal length of each material will be required. 

It frequently occurs in fancy novelty yarns that threads of 
viiequal she are twisted together. If a No. GO thread and a No. 
40 thread are twisted together, the count of the doubled thread 
will not be the same as if two threads of No. 50 have been 
twisted. For instance, when 60 hanks of GO's worsted are used 
GO hanks of 40's worsted will also be used, and when these have 
been twisted together there are still only GO hanks, but GO hanks 
of the former count weigh one pound, while GO hanks of the latter 
weigh 1^ pounds, consequently the GO hanks of twisted threads 
equal 2.5 pounds. 

Rule i6. The product of the given counts divided by their 
sum, gives the new count of twisted yarn, 

60X40 2,400 ^^ ^^ 
^60 + 40 = TOO" = ^0- 24 worsted. 

Some allowance must be made for take-up or contraction in 
twisting, but this will vary with the number of turns of twist per 
inch in the yarn and the diameter of the threads. 

Take-up, contraction, and shrinkages are not considered in 
these examples. 

Rule 17. When three or more unequal threads are twisted 
together, the counts of the resulting twist thread is found by 
dividing the highest count by itself and each of the given counts 
in succession; the quotient in each case representing the propor- 
tionate weight of each thread. Then dividing the highest counts 
by the sum of the quotients, the answer will be the new counts. 

Example. Find the counts of a 3-ply thread composed of 
one thread each of 20's, 30's, and GO's cotton. 

GO ^ GO = 1 

GO ^ 30 = 2 GO -^ G = lO's, count of 3-ply cotton thread. 
GO ^ 20 =^ 
T 

Find the counts of a 3-ply thread composed of one thread 
each of 120's, GO's, and 40's cotton. 



TEXTILE CALCULATIONS 15 

Compound Thread Composed of Different Materials. It is 

obvious that when threads composed of different materials are 
twisted together it is necessary to first reduce all to the denomina- 
tion of the yarn system in which it is required. 

Suppose a compound twist thread is made up of one thread 
of 24:'s black worsted, one thread 16's red cotton, and one thread 
8's green cotton. Find the equivalent counts in worsted as follows: 
840 X 16 = 13,440 -^ 560 = 24 worsted. 
840 X 8 = 6,720 -^ 560 = 12 " 
24 -^ 24 = 1 

24 ^- 24 = 1 24 -^ 4 = 6's, counts of 3 -ply thread in worsted. 
24 ^ 12 =2_ 
4 
What is the equivalent in a single woolen thread of a 3-ply 
yarn composed of 10.5 run woolen, 20's cotton, and 30's worsted ? 
840 X 20 = 16,800 ^ 1,600 = 10.5. 
560 X 30 = 16,800 -^ 1,600 = 10.5. 
10.5 -^ 3 = 3.5 run woolen. 

EXAMPLES FOR PRACTICE. 

1. If a thread of 20's and a thread of 40's single worsted 
be twisted together, what is the resultant counts ? 

2. What is the resultant counts [a) of 30's and 60's cotton 
twisted together, (^) of 30 lea and 60 lea linen twisted together, 
and («?) of 30's and 60's worsted twisted together ? 

3. A 3-ply thread is made by twisting the following yarns: 
one thread 10^ run woolen, one thread 30's worsted, one thread 
20's cotton. What would be the equivalent counts of the com- 
pound thread in (a) single cotton, (J) woolen cut, (c) single worsted, 
and (d) woolen run ? 

4. Give the resultant counts of 36'8, 45's, and 54's worsted 
yarn twisted together. 

5. How many hanks would there be in 1 pound of 2-ply 
yarn made by twisting one thread of 32's cotton and one thread 
44's cotton together ? 

6. Given 36 metric cotton counts, find the equivalent counts 
when twisted with a60-2 spun silk, the answer to be in cotton counts. 

7. What would be the resultant counts in spun silk of 30's 
worsted, 20-2 spun silk twisted together ? 



16 TEXTILE CALCULATIONS 



twisted together. 



8. Find the equivalent counts of 20'8, 82^8, and 50's worsted 
ed together. 

9. A thread is composed of two tli reads 4()'s worsted, and 
one thread 80's-2 spun silk. Find the e(piivalent counts in cotton. 

10. Find the resultant counts of 70's, 60's, 40's, and 20's 
cotton twisted together. 

FANCY AND NOVELTY YARNS, 

Novelty yarns, such as knop, spiral, loop, corkscrew, chain, 
etc., are made from various lengths of threads, and consequently the 
previous rules will not apply in all cases. If there is no variation 
in lengths, the same number of hanks will be required of each 
kind of yarn, but when lengths vary, the counts of the twisted 
threads will also vary according to the several modifications of 
take-up in the material used. 

For example, if it is desired to make a fancy yarn from three 
different counts of yarn, say 40's, 30's, and 20's cotton, the take-up 
in each case being equal, what length and weight of each material 
is necessary '( 

Rule i8. First, find the necessary number of pounds of each 
yarn to give equal length, by dividing the highest counts by itself 
and the counts of each of the others, the result being the relative 
weight required of each. 

40 ^ 40 = 1 pound. 
(A) 40 -^ 30 = IJ pounds. 

40 ^ 20 =: 2 pounds. 

The respective weights of the yarn multiplied by their counts 
will give the required number of hanks of each. 

1 pound X 40 = 40 hanks of 40's cotton. 
(B) 11 pounds X 30 = 40 hanks of 30's cotton. 

2 pounds X 20 = 40 hanks of 20's cotton. 

It is obvious that if a certain length of twist is required the 
yarns used must be of approximately the same length, whatever the 
counts, but when the take-up varies, the conditions are more or 
less complicated. 

Suppose a novelty yarn is made by twisting two threads of 
40's red cotton, one thread of 30's green cotton, and one thread 



TEXTILE CALCULATIONS 17 

of 20's black cotton, and the relative lengths of material used are 
7, 5, and 4 inches respectively. Find the counts of the combined 
thread. The last named thread is straight or 100 per cent. 

First, find the take-up of each yarn by dividing each relative 
length by the straight or 100 per cent thread. 

7 -^- 4 = 1| take-up. 
(C) 5 -f- 4 = 11 '' '' 

4^4=1 " " 

The number of hanks of each (obtained by A and B) multi- 
plied by the take-up (obtained by C), will give the number of hanks 
of the respective yarns necessary for the twist yarn. 

40 X If = 70 hanks of No. 40 

40 X 1| = 70 hanks of No. 40 

40 X IJ = 50 hanks of No. 30 

40 X 1 =40 hanks of No. 20 

and these divided by their relative counts, will give the weight 
of each. 

70 hanks -f- 40 = 1.75 pounds. 

70 hanks -^ 40 = 1.75 pounds. 

50 hanks -f- 30 = 1.66 pounds 

40 hanks -^ 20 == 2.00 pounds. 
7.16 pounds. 

The number of hanks necessary for equal length divided by 
the sum of their weights will give the count of the combined or 
resultant thread. 

40 -f- 7.16 =- 5.58 count. 

To prove, find the length of each yarn in one hank of the 
novelty yarn thus, 

7 inches No. 40's = 840 X If = 1,470 yards. 
7 inches No. 40 = 840 X If = 1,470 yards. 
5 inches No. 30 = 840 X IJ = 1,050 yards. 
4 inches No. 20 = 840 X 1 = 840 yards. 
The weight of each being 

No. 40 = 1,470 X 7,000 -f- 40 X 840 = 306.25 grs. 
No. 40 = 1,470 X 7,000 -^ 40 X 840 = 306.25 grs. 



18 ^jExtile calculations 



No. :J.) : 1,050 X 7,000 -- 30 X 840 == 201.00 grs. 
No. 20 = 840 X 7.000 -f- 20 X 840 = 350.00 grs. 

1,254.10 grs. 

Therefore, if one luink of the novelty yarn weiglis 1,254.16, 
the eoiints will be 7,000 ^- 1,254.16 = 5,58 counts, the same 
as given in the above example. 

WEIGHT OF MATERIAL TO PRODUCE A GIVEN WEIGHT. 

The question of determining the actual quantity of each kind 
of yarn required to produce a given weight of ply or folded yarn 
is an important item in textile calculations, and may assume 
a variety of forms. The simplest form is to assume that the 
counts of the yarns and the total weight are given, and it is re- 
quired to find the weight or quantity of each yarn to produce the 
total weight. For convenience, assume that the counts of the 
yarns to be twisted together are 30's and 20's respectively, and 
that the total weight required is 1,000 pounds. 

The first step is to ascertain the counts of the folded yarn 
resulting from this combination, after the manner already 
described, thus 

30 X 20 



30 + 20 



12's. 



After this the process is quite simple, being a question of 
proportion, or, as each count in succession is to the count of the 
folded yarn, so is the total weight to the required weight. To make 
it clear, the counts of single yarns are 30's and 20's respectively, 
the folded yarn is 12's, and the total weight 1,000 pounds, then 

30 : 12 :: 1,000 : X = 400 pounds of 30's yarn. 
20 : 12 :: 1,000 : X = 600 pounds of 20's yarn. 

So that the whole is reduced to the simplest possible form. 

Rule 19. To find the weight of each material required to 
produce a given weight of a double and twisted or compound 
yarn. First ascertain the counts of the two yarns twisted together 
after the manner laid down in Rule 16, then as each count in suc- 
cession is to the compound yarn, so is the total weight to the 
weight required. 



TEXTILE CALCULATIONS 19 



Example. What amount of each kind of yarn is required to 
produce 1,000 pounds of twist yarn made from 60's and 80's 
cotton? 

60 + 80 ~ ' 
60 : 34f :: 1,000 = 571f 
80 : 342 :: i,000 = 428^ 

17)00 
Proof. 

80 X 840 = 67,200 yards X 428-4- = 28,800,000 yards. 
60 X 840 = 50,400 '• X 571f = 28,800,000 yards. 
The following rule is used in many mills: 

(a) Given weight X lower count ^tt • i pi -, - ^ 

^ ^ -^ s — ^ = W eight or the higrher count. 

bum or the two counts ® ^ 

ih\ Given weight X higher count att • i v i 

^ ' -^ , ^ — ^ = Weight or lower count. 

iSum of the two counts ^ 

Example. What amount of material will be required for 
each thread to produce 250 pounds of double and twist yarn made 
from 32's and 40's worsted ? 

250 X 32 -^ 72 = 111-J- pounds, weight of higher count. 
250 X 40 ^ 72 = 138|- pounds, weight of lower count. 
Proof. 

32 X 560 = 17,920 X 138f = 2,488,888-| yards. 
40 X 560 = 22,400 X 111^ = 2,488,888f yards. 
When only two counts are required, the above methods are 
simple and very useful, but when three or more counts are twisted 
together, some other method of solution is necessary to find the 
weight of each material to produce a given weight. 

Rule 2o. First find the relative w^eight of each kind of yarn 
by dividing the highest count by its own number and the other 
numbers in succession, then multiply the given w^eight by the 
relative weight of each count, and divide by the sum of the relative 
weights. The quotients w^ill be the weights of each kind of yarn. 
Example. 533 pounds of twist to be made from 20's, 30's, 
and 40's; required the weight of each. 

40 -^ 40 = 1 X 533 = 533 -^ 41 = 123 pounds. 
40 ^ 30 = 11 X 533 
40 -^ 20 = 2 X 533 
4-1 



710S 


^4i = 


= 164 pounds. 


,066 


^H- 


= 246 pounds. 
533 



20 TEXTILE CALCULATIONS 



Kx}ini|)l(\ 120 pounds of twist is required of 80's, 40's, and 
()()'s worsted. Wliat weio;ht of each count will the compound 
thread contain^ 

To Find the Relative Weight of Each Thread in a Com= 
pound Yarn When Lengths Vary. By llule 18, both the result- 
ant counts and the relative weight of the two yarns may be obtained. 
Exam])le. A fancy loop yarn is composed of 12's and 60's 
worsted, () inches of the latter being required to 3 inches of the 
former. AVhat weight of each will be required to produce 200 
pounds of twist, and what number of hanks of the loop yarn will 
weigh 1 pound ? 

Note— The length of GO's is double that of the unit length of 12's. 
GO + CO = 120 -^ 60 = 2 pounds. 
00 + = 60 ^ 12 =-- 5 " 

7 pounds, 
or 
60's = 6 ^ 3 = 2 X 60 = 120 hanks. 
12's = G ~ 6 = 1 X 60 = 60 " 
120 -^ 60 = 2 pounds of 60's. 
60 -^ 12 = 5 pounds of 12's. 
()() hanks of twist yarn weigh 7 pounds. 60 -^ 7 = 8.57 
hanks = 1 pound, using Rule 20 as in previous example. 

(a) 200 X 2 

^ ^ y- -= 57+ pounds of 60's. 

(^) 200X_5 ^ ^^^^ p^^_^^^ ^^ ^^,^ 

Example. A loop yarn is composed of 2 threads of 8's 
worsted and 1 thread of 12's worsted; 21 inches of the former are 
required to 14 inches of the latter. What weight of each will be 
recpiired to produce 150 pounds of twist, and w^hat number of 
hanks per ])ound will the loop yarn contain ? 

12 -f- (4 of 12) = 18 -^ 8= 2.25 pounds. 
12 + (i of 12) = 18 -^ 8 = 2.25 '' 
12 4- " = 12 ^ 12 = jL 

5.5 pounds. 
Twelve hanks of loop yarn weigh 5.5 pounds. 

12 -f- 5.5= 2j\ hanks per pounds or loop counts. 



TEXTILE CALCULATIONS 21 

and 150 X 2.25 ^ 5.5 = Ql^\ of 8's worsted. 
150 X 2.25 -^ 5.5 = Gl-,\ of 8's '' 
150 X 1 -^ 5.5 = 27-^3^ of 12's " 

150 pounds of loop yarn. 

To Find the Weight of a Given Yarn to be Twisted With 
a Yarn, the Weight and Counts Being Known. The problem 
may now be put in a different way. There may be a given 
quantity of one of the yarns, and it is required to find what 
weight will be necessary to twist with it and just use it up. 
This is obviously the reverse of the above proceeding, and at once 
resolves itself into a simple proportion, being dependent only upon 
the relative counts; thus 20's and 30's are to each^ other as 2 is to 
3, and, as the higher number is the lighter yarn, the proportion 
must be inverse. 

Supposing then, that there are 400 pounds of 30's yarn and 
it is required to find how much 20's would be necessary to twist 
with it. The problem would be as 20 : 30 :: 400 : X = 600. 
Proof: 600 pounds of 20's would contain 600 X 20 = 12,000 
hanks, and 400 pounds of 30's would contain 12,000 hanks, so 
that the length of each would be equal. 

Rule 21. Multiply the'given weight by its counts and divide 
by the counts of the required weight and the quotient will be the 
weight required. 

Example. If you have 480 pounds of 30's cotton, what 
weight of 26's cotton would be required to twist with it to work 
it all up, and what will be the counts of the resulting twist ? 

480 X 30 ^ 26 = 553ii pounds. 

26 X 30 ^ ^ 

25 ^ 3Q = l^TT «o^"ints. 



Proof. 



480 X 30 = 14,400 hanks. 
553|i X 26 = 14,400 hanks. 



AVERAGE COUNTS. 

When average counts are required, it is assumed that .the 

threads are contiguous in the woven fabric and retain their 

respective individualities, e.g., when two or more threads of 



22 TEXTILE CALCULATIONS 

various sizes aro usi^d side by side in a fabric. It is frequently 
necessary to determine the average counts of these threads, that is, 
the counts which will represent the same weight and length for 
the combination of several yarns employed in the woven fabric. 
Suppose a cloth is woven with the pattern as follows: 2 tlireads of 
go's cotton, and 1 thread of 20's cotton. What is the average 
counts i 

Rule 22. Multiply the high count by the number of threads 
of each count in one repeat of the pattern. 

60 X 2 = 120 hanks. 
60 X 1 = 60 " 

Divide each product separately by the given counts. 

120 -- 60 = 2 pounds. 
_60 ^ 20 =- 3 " 
180 5 pounds. 

Divide the total number of hanks by the sum of these quotients. 

180 H- 5 = 36 average counts. 

Rule 23. To find the average counts when any number of 
threads of different counts are used in the same cloth. Divide 
the product of the counts by the sum of the unequal counts, then 
multiply by the number of threads in one repeat of the pattern. 
The answer is the average counts. 

A sample is composed of 1 thread of black 16's cotton, and 
1 thread of white 4:0's cotton. Find the average counts. 

40 X 16 = 640 

1 ft -4- 4.0 ^Pt ~ ^^'^^ ^ ^— 22.86 average counts. 

The threads are laid side by side in the pattern, and each 
one retains its individuality, therefore, the average weight of the 
threads is half that of the compound thread, or the average counts 
is double the counts of the compound thread. 

A pattern is composed of 2 threads of 40's black cotton, and 1 
thread of 16's red cotton. Find the average counts. 



TEXTILE CALCULATIONS 23 

A sample is composed of 1 thread of black 16's cotton, and 1 
thread of white 40's cotton. Find the average counts. 

40 X 16 := 640 ^ ^^^g X 2 = 22.86 average counts. 
K) -f- 40 =56 ^ 

The threads are laid side by side in the pattern, and each one 
retains its individuality, therefore, the average weight of the 
threads is half that of the compound thread, or the average counts 
is double the counts of the compound thread. 

A pattern is composed of 2 threads 40's black cotton, and 1 
thread 16's red cotton. Find the average counts. 

40 X 2 =: 80 80 -^ 40 = 2 

40 X 1 = 40 40 -^ 16 :^ 2.5 

I20 4.5 

120 -T- 4.5 = 26.66 average counts. 

40 ^ 40 =1 
40 -^ 40 =1 
40 -^ 16 = 2_^ 
4.5 
40 -^ 4.5 = 8.88 8.88 X 3 = 26.64 average counts. 

A pattern is composed of 4 threads of 80's white cotton, 2 
threads of 40's black cotton, and 1 thread of 16's red cotton. 

Find the average counts. 

80 ^ 80 = 1 X 4 threads = 4 

80 -^- 40 = 2 X 2 threads = 4 

80 -^ 16 = 5 X 1 thread = 5 



7 13 

80 X 7 

^-^ — = 43^ average counts. 

Proof. Obtain the weight of one hank of each count given, then 
the weight of an average hank with the threads of the proportion 
given, and find what would be the counts of that weight. 

1 hank of 80's = 7,000 -r- 80 = 87.5 grains. 

1 hank of 40's = 7,000 -^ 40 = 175. grains. 

1 hank of 16's = 7,000 ^ 16 = 437.5 grains. 

80 = 87.5 X 4 = 350 

40 = 175. X 2 = 350 

16 = 437.5 X 1 := : 437.5 

7 1137.5 grains. 



24 TEXTILE CALCULATIONS 

1137.5 -^ 7 = 1G2.5 grains average. 
7,000 grains ^ 102.5 = 43.^ average counts. 

UNKNOWN COUNT IN A COMPOUND OR TWIST THREAD. 

Occasionally, it happens that a manufacturer or spinner has 
given to him the counts of a novelty or fancy twist yarn, also the 
counts of one or more of the threads of which it is composed. It 
then becomes necessary to find the size of the unknown thread 
which, together with the known counts, makes the compound 
twist yarn. 

Rule 24. To find the required counts of a single yarn to be 
twisted with another, the counts of which is already known, to pro- 
duce a compound or twist thread of a known count. Multiply the 
counts of the known single thread by the counts of the compound 
or twist thread, and divide the product by the known counts of the 
single thread minus the known counts of the compound thread. 
The quotient will be the counts of the required single thread. 

Example. Having some yarn in stock, the counts of which 

is 1-30's cotton, it is desired to produce a compound or twist thread 

equal to 1-12's cotton. Find the count of the required thread. 

30 X 12 360 ^^.„ . . ^, . 

-— -— =: = 20's required thread. 

30 - 12 18 ^ 

Proof. 30 X 20 600 ,ow • . a .^ a 

I4J s twist or compound thread. 



30 + 20 ~ 50 

In the cotton trade, worsted and silk threads are twisted with 
cotton. In the worsted trade, cotton and silk threads are twisted 
with worsted. In the woolen trade, cotton, silk, and worsted 
threads are twisted with woolen. 

For the cotton trade, transfer the worsted and silk to cotton 
counts. For the worsted trade, transfer the cotton and silk to 
worsted counts. For the woolen trade, transfer the cotton, silk, 
and worsted to woolen numbers. 

Rule 25. Two known single thread, a third thread required 
to produce a known compound thread. First find the size of the two 
known threads twisted together, then proceed as in previous examples. 

Find the counts of the third thread to twist with a 1-30's cot- 
ton thread, and 1-00's cotton thread, to produce a three-ply thread 
equal to a X^'§ cotton. 



TEXTILE CALCULATIONS 



60 X 30 = 1,800 

60 + 80 = ^"90" - ^^'^ ^^"^^^• 

20 X 12 = 240 

20 _ 12 ^ ~8~ ~ ^^'^ required. 

Proof. Three-ply twist, 60's, 30's and 30's. 
60 -f- 60 = 1 

60 ^ 30 = 2 60 ^ 5 = 12's 3-ply thread. 
60 -^ 30 =. 2 
5 
Find the size of a worsted thread to twist with a 1-30's cotton, 
to produce a two-ply thread equal to a 2 -30's cotton. 

2-30's =l-15's cotton. 

30x15 = 450 

30 - 15 = 15" == ^^'^ ^^"^"• 

840 X 30 = 25,200 

25,200 
KgQ = 45's required worsted thread. 

EXAMPLES FOR PRACTICE. 

1. A pattern is composed of 4 threads of 80's black worsted, 
3 threads of 60's white worsted, and 1 thread of 16's blue worsted. 
Find the average counts. 

2. Find the counts of the required thread to twist with a 
40's cotton to produce a compound thread equal to a 24's. 

3. Find what counts twisted with 24's cotton would produce 
a compound thread equal to a 9's cotton. 

4. Required the counts of a spun silk thread to twist with a 
20's cotton and a 30's worsted to produce a 3-ply thread equal to 
a 3^-run woolen. 

5. Find the counts of a third thread to twist with a 30's cot- 
ton, and a 20's cotton to produce a 3-ply thread equal to a 12's 
cotton. 

CONSTANTS. 

In figuring textiles there are uiany numbers which are con- 
stantly repeated, thus making it desirable to dispense with some of 
them by cancelling one into the other, for instance: 7,000 h- 840 
7;000 -i- 1,600. 7,000 -h 560, etc. 



26 TEXTILE CALCULATIONS 

Those luiinbers are also used in reverse order, one l>eing 
multiplied by, or divided into, the other very frequently. To 
simplify these calculations, the following constants have been 
worked out and will prove a valuable reference table: 

Long Method First Constant Second Constant. 



Woolen 7,000- 


- 1,600 = 


4.375 - 


-36 = 


.1215 


Worsted 7,000 - 


- 560 = 


12.5 - 


-36 = 


.3472 


Cotton 7,000 - 


- 840- 


8.33 - 


- 36 = 


.2314 


Linen 7,000 - 


- 300 = 


23.33 - 


- 36 = 


.648 


Woolen 1,600 - 7,000 = 


.228 






Worsted 560 - 7,000 = 


.08 






• Cotton 840 - 7,000 = 


.12 






Linen 300 - 


- 7,000 = 


.043 







Fi'equently the counts of a very small amount of yarn is re- 
quired, and to obtain the necessary data, a pair of fine grain scales 
is one of the most necessary pieces of apparatus required in a 
manufacturer's or designer's office. 

Suppose a sample of woolen cloth contains 40 threads per inch 
and the sample is 2 inches long, then there w^ould be 40 X 2 = 80 
inches of yarn, and these threads weigh 2.5 grains. What is the 
run of the yarn ? 

Rule 26. Multiply the number of inches of yarn by 7,000 
(the number of grains in 1 lb.), and divide by the weight (in grains) 
of the yarn, multiplied by the standard number, and by 36. The 
answer will be the run of the yarn. 

80 X 7,000 _ 
2.5 X 1,600 X 36 - ^'^^ ''''''• 

Example. If a sample of cotton cloth 1 inch long has 40 
warp threads in 1 inch, and the yarn weighs 2.5 grains, w^hat is 
the count? 

40 X 7,000 
2.5 X 840 X 3 -6-- ^"'^'^Q^^- 

Explanation. As there are 7,000 grains in'l lb. and 840 
yards of number 1 yarn in 1 lb. 7,000 -^ 840 gives the number of 
grains in one yard of number 1 yarn, or 8^ grains. The constants, 
as we have 40 warp threads per inch, 8J grains, multiplied by 40 
gives us the weight in grains of one running yard of number 1 
warp one inch in width, or 333-J grains. 



TEXTILE CALCULATIONS 27 



As one square inch of warp weighs 2.5 grains, one running 
yard one inch wide would weigh 2.5 X 36 = 90 grains. Now, as 
90 grains is the actual weight of the yarn, and 333| grains the 
weight of an equal quantity of number 1 yarn, the number of our 
warp yarn is the number of times the weight of number 1 yarn is 
greater than the given yarn, or 

333.33 -f- 90 = 3.7037 cotton counts. 

Example. Supposing 12 threads worsted were obtained, each 
36 inches long with a total weight of 1 grain, what is the counts? * 

' = 12.5 grains, the weight of 1 yard of number 1 worsted. 

Therefore, if 1 yard of yarn weighs 12J grains, the counts are I's, 
or if 2, 3, 4, or 5 yards weigh 12^ grains, the counts are 2's, 3's, 
4's, or 5's respectively, or the number of yards of yarn which weigh 
12 J grains is equivalent to the counts in worsted. 

Then the counts in the above example would be number 12^, 
because 12^ yards would be required to weigh 12J grains. 

If 48 inches of woolen yarn weigh 2 grains, what is the run? 

48 X 7,000 ^ ^^ , 

Long method. ' 9^1 600 V ^(^ ^ ^-916, say 2.9 run. 

48 X 4.375 
First constant. o \/ S6 — ~ 2.916 run. 

48 X .1215 
Second constant. o — 2.916 run. 

. If 96 inches of cotton yarn weigh 2 grains, what is the counts ? 

96 X 7,000 
Long method. ^ y §49 ^ 35 = H-l^ counts. 

96 X 8.33 
±irst constant. ^ x 36 ~ H.IO counts. 

r, . , 96 X .2314 

Second constant. ^ = 11.10 counts. 

If 75 inches of worsted yarn weigh 2.5 grains, what is the 
count ? 

^ , 75 X 7,000 
^""g ^^'^"^- 2.5 X 560 X 36 = ^^'^^^ ^«^^^^- 
*NoTE— This subject is again taken up in Yarn Testing. 



TEXTILE CALCULATIONS 



75 X 12 5 
First constant. 9 5 y tjf = 10.410 counts. 

75 X .3472 
Second constant. ^ z= 10.416 counts. 

YARN TESTING, 

The term " Yarn Testing" means a great deal more than the 
cMsual observer in a mill supposes. Failure to test yarn, or im- 
perfect testing may cause serious trouble. It is often necessary to 
test yarns in a variety of ways, and for different purposes. The 
most common test, and it may be safely said the only test which is 
applied in a large number of mills, is to ascertain the counts, but 
there are instances when the yarn should be tested for strength, 
elasticity, evenness, and for quality. 

This latter test in some cases is a difficult one, and the ques- 
tion often arises as to what is meant by quality. As applied to 
yarns, the term quality is difficult to define briefly and accurately, 
in fact, it may almost be said that it cannot be defined, because as 
applied to different classes of yarn it has altogether different mean- 
ings. Without attempting to give definitions, an effort will be 
made to show what the different qualities or characteristics of yarn 
comprise, and so ascertain what tests are necessary to decide their 
suitability for the purpose to which they are to be applied. 

The first step in yarn testing is to test the counts, which means 
to find the weight and size of the yarn. As previously explained, 
there must be some standard measurement or weight, and some 
means of determining the bulk or quantity of yarn. In this case 
the determination is based upon the length of yarn in a given 
weight, as, for instance, the number of yards per pound, ounce, or 
grain; but in different yarns and different sections of the country, 
this is a variable quantity. For example, the counts of cotton are 
figured by hanks per lb., and the hank contains 840 yards. Worsted 
is also figured by the hank, but the length of yarn is 560 yards. 
The basis of linen calculations is the lea, which is practically equiv- 
alent to the hank, but contains 300 yards. Woolen is reckoned 
in a variety of ways, but chiefly by 1,600 yards to the pound. 

There appears then to be only one way of dealing w4th this 
subject so as to meet the requirements of students of different dis- 



TEXTILE CALCULATIONS ^ 

tricts, and that is, to deal with it on general lines, and illustrate 
with examples from the best known and generally recognized sys- 
tem of counting yarns, and in such a manner that the student can 
readily adapt himself to any^' other system. 

Testing for Counts. The process of testing for counts in the 
cotton and worsted systems, in which the method of indicating the 
count is general, may now be explained. In testing these yarns in 
the mill, there are two systems in use; one by what is known as 
the '''quadrant", which is a balance with a graduated scale and upon 
which a certain number of yards is placed, when a pointer indicates 
the counts; the other system is by weighing with an ordinary fine 
balance and grain weights. The latter test is frequently done in a 
careless manner and very inferior balances employed, with the 
result that the tests are very unsatisfactory. 

The ''quadrant'''^ arrangement is very useful because the in- 
dicator shows the counts the moment the yarn is put on the hook. 
The arrangement is very simple in principle, being in fact nothing 
more than an adjusted balance or lever. If it is arranged for cot- 
ton or worsted, the two arms of the lever, that is, the hook end and 
the indicator respectively are so balanced that one is, say, seven 
times the weight of the other, or more properly speaking that their 
relation to each other and to the scale is as 7 to 1. Then, if -i of a 
hank is placed upon the hook, the indicator is at once brought to 
the point on the scale which shows the number of hanks per pound. 
When cotton is to be tested, 120 yards are measured off and placed 
upon the balance, and the pointer at once indicates the counts; if 
worsted, 80 yards are measured off and balanced with a similar 
result. 

It must be clearly understood that the "quadrant" balance is 
always made for a given class of work, and to weigh a given num- 
ber of yards; it is not usually made so that it can be applied to 
every purpose, but, like most special machines, must be applied to 
the testing of a specified class of yarn, and a specified number of 
yards weighed. Of course, the operator may vary this with a little 
ingenuity, but this would involve calculations, and consequently 
the machine would lose its advantages. 

Reeling. By this system any length of yarn may be reeled 
off and weifi^hed and the exact counts found by calculation. 



do TEXTILE CALCULATIONS 

This operation is carried on by means of a reel; one of the best ex- 
amples of which is shown at P^ig. 1. A sufficient length of yarn 
can be readily measured on this machine to test the counts to the 
greatest degree of accuracy. 

The reel is 54 inches, or one and one-half yards, in circum- 
ference, and the dial is graduated into 120 parts to indicate the 
number of yards reeled from each spindle. While feeding yarn 
upon the reel, the yarn guides and the spindles are kept in line 
with each other, this being very desirable, in fact, necessary 
when reeling fine yarns. The extra length of the yarn guides is 
useful in increasing the friction upon the yarn by taking a half 
turn or more around them. The automatic feed motion lays the 
yarn flat upon the reel, thus securing accurate and uniform measure- 
ment, and consequently correct results as to stretch, strength, and 
numbering. When the skein is taken off the reel, it is weighed 
and the counts calculated from the weight. 

It is a common practice to reel yarn upon a machine of very 
inferior construction, and in a very rough manner, which of course 
produces doubtful results. For example, in reeling worsted yarns, 
it is a common practice to use a reel with a circumference of one 
yard, and which does not distribute the yarn in the manner indi- 
cated. The number of yards which will correspond to the intended 
counts of the yarn is measured off by counting the turns of the 
reel, then this yarn is weighed in a common apothecaries' balance 
against a weight of 12 J grains, and if it balances or approximately 
balances the 12^ grains, it is said to be of the counts indicated by 
the number of yards weighed. Similar systems are sometimes used 
in the cotton and woolen industries, and, in some cases, the meth- 
ods are, if possible, even more crude. But, although this is the 
common practice, it is not sufficient for good work, therefore, we 
must have more complete systems. 

The first question which suggests itself is, how is the 12^ 
grains found to be the constant weight, and what weight would 
be employed for other yarns ? The grain weight, being the 
lowest of the recognized standard weights, is made iise of, and as 
there are 7,000 grains in one pound (Avoirdupois), this is divided 
by 560 (the number of yards in one hank) which gives 12^. For 
cotton 8 J grains would be the constant; for woolen, 4| grains. 



il Vv\ 



TEXTILE CALCULATIONS 



31 



How to ascertain the numhev of cotton yarn. Keel, or 
measure of?, and weigh 9, 18, 30, 90, or any number of yards of 
tlie yarn, observing that the greater the number the more accurate 
the result will be. 

Rule 27. Multiply the number of yards by 8J and divide 
the product by the weight of the sample in grains; the quotient 
will be the number of the yarn, i.e.^ the number of hanks in a 
pound. 

Example. Suppose 9 yards weigh 5 grains; then 9x8^ = 




Fig. 1. Brown & Sharpe Yarn Reel. 



75. 75 ^- 5 = 15's, the number of yarn, i.e., the number of 
hanks to a pound. 

Rule 28. To ascertain the mimher of linen yarn. Reel, or 
measure oif, and weigh 9, 18, 30, 90, or any number of yards, the 
greater the number the more accurate the result will be. Multiply 
the number of yards by 23^ and divide the product by the weight 
of the sample in grains; the quotient will be the number of the 
yarn. 

Examples. Suppose 12 yards weigh 17-| grains; then 12 X 
23^ = 280. 280 -^ 17^ = 16, the number of counts per pound. 
Suppose 9 yards weigh 5 grains; then 9 X 23^ = 210. 210 ^- 
5 = 42, the count of the yarn. 

Rule 29. To find the numher of worsted yarn. Reel, or 
measure off, and weigh 9, 18, 30, 90, or any number of yards, 
the greater the number the more accurate the result will be. 



32 



TEXTILE CALCULATIONS 



Multiply tlu' yMi'cls by 12^ and divide the product by the weight 
of the sample in grains; the (piotient will Ije the number of the 
yarn, i.e., the number of hanks or skeins to the pound. 

Example. Suppose 9 yards weigh 5 grains; then 9 X 12J 
= 112.5. 112.5 ^ 5 = 224, the number of the yarn. 

Rule 30. To find the run or mcmher of woolen yarn. lieel, 
or measure off, and weigh any number of yards of the yarn, ob- 
serving that the greater the number the more accurate the result 
will be. Multiply the number of yards by 4| and divide the product 




Fig. 2. Sample Scales. 



by the weight of the sample in grains; the quotient will be the 
number of hanks per pound. 

Examples. Suppose 90 yards weigh 45 grains; then 90 X 
4§ = 393.75. 393.75 -- 45 = 8|, the number of run of the yarn. 
Suppose 9 yards weigh 5 grains; then 9 X 4.375 ^= 39.375. 
39.375 -T- 5 =: 7.875 or 7|, the number of the yarn. 

The common practice in testing yarns is what might be termed 
a rough and ready one, yet it is often considered sufiicient in ordi- 
nary practical work, but for good analysis a more perfect and 
delicate system must be used. 

Suppose, for instance, that it is required to reproduce a cloth, 
or for any purpose to make a complete analysis of it. The opera- 
tion ought to be conducted w^ith as much care and nicety as a 
chemist makes a quantitative analysis; in fact, it must be a quan- 
titative analysis. The counts of the yarn must be ascertained with 



TEXTILE CALCULATIONS 



the greatest degree of exactitude, as well as the different quantities 
of the material employed, threads and picks per inch, etc., and if 
only a small piece of cloth is available, there must be careful work. 
Of course, by long experience and careful observation, a manufac- 
turer may guess, or, as he terms it, "judge" with a degree of ac- 
curacy what the yarn is, but this is not accurate enough. lie may 
have to try many experiments, some of them costly, before he ar- 
rives at the result desired, whereas a system of analysis, carefully 
carried out, will give him results at once. This applies at present 
to testing yarns for counts, and ascertaining the number of threads 
per inch in a sample, but it will apply to other systems which will 
come under notice in due time. Then as to the requisites for this 
work. 

Scales. The first and most important is a good balance. Of 
these there are many styles which weigh to different degrees of ac- 
curacy. Small balances or scales may be had for a few dollars, 
and for a student who cannot give more for his own private use, 
they are better than nothing, certainly better than trying to guess 
the counts of yarn. A good balance, and one which may come 
within the students' reach is shown at Fig. 2. These balances are 
made to work with the utmost degree of accuracy, and will weigh 
one pound by ten thousandths of a pound. 

The scales illustrated at Ficr. 3 are still better, however, as 
they weigh by the grain system. These scales will weigh one 
pound by tenths of grains, or one seventy thousandth part of one 
pound Avoirdupois, which makes them especially well adapted for 
use in connection with yarn reels, for the numbering of yarn from 
weight of hank, giving the weight in tenths of grains to compare 
with tables. 

These scales can be had to weigh by the metric system to 
-j-i-g gram, being supplied with weights of 1, 2, 5, 10, 20, 40, 60, 
100, and 200 grams. 

When the testing is merely for percentages, the gram weights 
are the most convenient, as they are based upon the decimal system, 
but where it is a question of ascertaining the counts of yarn or the 
weight of cloth, the grain weights are the best to use. "With the 
above series of scales and weights, tests can be carried out to 
almost perfect accuracy. 



M 



TEXTTT.E CALCULATIONS 



When ;i very small quantity of yarn is available, say one or 
two yards, it must be weighed with great care. Of course, when 
a large quantity is available, find now many yards will weigh 12J 
grains, if the yarn is worsted; 8 J grains if cotton; and so on for 
other yarns, according to the system of counting. Suppose, for 
instance, that it is required to test the yarn in a cloth, and only a 
small piece can be obtained, say two or three square inches. This 




Fig. 3. Brown & Shai-pe Scales. 



must be measured carefully, and as many threads taken out as will 
make one yard, two yards, or as mnch as possible. For example, 
let it be two yards of worsted weiizhino- 1 3 9 m-ains. Find the 



oV g^-^ 



counts. If two yards weigh 1 -j^^^y grains, how many yards will 
weigli 7,000 grains ? Putting it in the usual form of a proportion 
as 1 y^g- : 7,000 : : 2 : 10,072 yards, or there are that number of 
yards in one pound. As there are 560 yards per hank in worsted, 
and the counts are indicated by the number of hanks per pound, 
the 10,072 must be divided by 560, thus 10,072 -- 560 = 18 
hanks nearly, then the counts would be called 18's, as it is near 
that number. If it were cotton, the same rule would apply, but 
instead of dividing by 560, the yards would have to be divided by 
840 thus, 10,072 -- 840 = 12 hanks, or equal to 12's counts. If 
it were woolen on the run system, it would be divided by 1,600, 
and so on for other varieties of yarn. In snch small quantities as 
this, there is always some slight liability to error, but with careful 
work this should not exceed 2 per cent. 



TEXTILE CALCULATIONS 3& 

The problem may be simplified by putting it in the form 
of an equation. Let Y represent the number of yards or length 
weighed, and W the weight in grains found. There are 7,000 
grains in one pound and a fixed number of yards per hank in the 
system upon which the yarn is counted, then 

7,000 X Y ' 

counts in worsted, 



5()0 X AY 
7,000 X Y 



counts in cotton, etc. 



840 X AY 

This may be further simplified as the 7,000 grains and the yards 
per hank are. constant numbers. Let the grains be divided by the 
yards per hank and find one constant number, thus for worsted 

7,000 
^ - g.w. = 12;V as tlie constant; for cotton 

5b0 - ' 

7,000 X Y 

— ^—j, — ^„ = 8* tor constant. 

840 X W -^ 

Kow let C represent the constant, and the formula will stand 

C X Y 

— == — = counts. 

TESTING BY COMPARISON. 

As w^e have said that in some mills yarns are tested by com 
parison, this lesson would not be complete without giving an idea 
as to the method employed. 

It consists in taking a few threads from the fabric, and these 
are crossed and folded over the same number of threads of somt 
known count, the two ends of each respective group of thread? 
being held between the fingers, the group of the unknown in one 
hand and the known in the other. The two groups are then 
twisted simultaneously so as to compare their relative diameters. 

Fig. 4 illustrates this method of comparing known with un- 
known counts. A represents the known and B the unknown 
counts. Take one, two or more threads of each kind of yarn and 
placing them together, as shown in the illustration, twist them, 
making, as it were, one continuous thread. By this simple act of 
twisting it is natural to make a comparison of the area and solidity 



TEXTILE CALCULATIONS 



of the threads. It is advisable to wet the yarns at the point where 
they are crossed, previous to twisting. During comparison, threads 
are added or taken from one or the other of the sets and again 
twisted as directed and compared until the two sets appear to make 
a similar thickness of thread. 

It follows that when the number of threads of a known count 
are of equal thickness to some other number of threads of unknown 
counts, these numbers bear a simple and direct proportion to each 
other. 




Fig. 4. Testing by Comparison. 

Example. 6 threads of 2-30's worsted are found by twisting 
and comparison to equal 8 threads of some unknown count. What 
is the count of the unknown threads ? 2-30's =: 15. Then as 
6 : 8 : : 15 : X = 20's, or 2-4:0's worsted i.e., 8 threads twisted 
together of 2-40's are equal in thickness to 6 threads 2-30's 
w^orsted twisted together. 

This method of testing is used practically, because a mill-man 
usually uses the nearest counts he has in stock to the counts of 
yarn in the sample to duplicate. Others do not trust to the eye 
when comparing yarns, but prefer to use a magnifying glass or 
microscope. 

Constants for Testing Yarns for Counts by Weighing Short 
Lengths of Cotton. 

1. 1,000 divided by weight in grains of 1 lea = counts. 

2. The number of inches that weigh 1 grain X .2314 = 
counts. 

3. Number of yards weighed -^ .12 X weight in grains = 
counts 

4. The number of strands of yarn, each 4y^g inches or 4.32 
inches long that weigh 1 grain = counts. 

5. The number of yards weighed X 8J -f- weight in grains 
= counts. 



TEXTILE CALCULATIONS 37 

STRUCTURE OF CLOTH. * 

Structure of cloth does not iiieau the fabric, nor the yarns 
from which the fabric is constructed, but it designates the materials 
from which the fabric is made, together with the system of inter- 
weaving. It has been explained that no woven fabric can be pro- 
duced without crossing, or interweaving at right angles, two distinct 
sets of threads. In the Instruction Papers on Textile Design several 
systems of interweaving are given and the meaning of plain or cot- 
ton weave, prunella twill, cassimere twill, basket or hopsack weave, 
five-harness sateen, etc., are explained. Now, the object is to find 
the quantity and hind of yarn, which, when used with certain 
weaves will produce a fabric of good structure. 

The ])lahi iceave is the simplest texture, requiring only two 
threads of warp and two picks of filling to complete the full weave. 
Not only is it the simplest, but it is the most limited in size. If 
two threads are drawn in on the same harness side by side, or two 
picks are placed in the same opening or shed, it is not a plain 
weave, and if one thread is taken away, the fabric is left without 
any means of binding or interweaving. 

Adding to the plain structure and only admitting of one ad- 
ditional thread and pick, we enter on the first lesson of figure and 
twill weaving, and the weave is designated as the three-harness 
tioill or prunella, tvjill. This is the first form of diagonal or rib 
effect at an angle of 45 degrees, and with the variations of this 
weave we can work out designs on a figured basis by twilling to 
the right for a number of threads and then reversing the twill, 
using either the warp-flush or the filling-flush weaves or combin- 
ing the two. 

The addition of one more thread forms the sioansdoion weave ^ 
which is a regular four-harness filling-flush twill, advancing one 
thread and one pick in regular consecutive order, forming a twill 
or diagonal at an angle of 45 degrees. We may say that with this 
number of threads, or this weave, the field for new combinations is 
unlimited, for with four harnesses, an endless variety of fabrics 
are constructed, such as dress goods, men's wear, etc. Weaves 
which repeat on four harnesses are very useful in cotton, woolen, 
and worsted manufacture. 

Adding one more thread and one more pick gives five threads 



TEXTILE CALCULATIONS 



in the warp, and five picks in the tilling; the smallest number on 
which a mteen weave may be constructed. There is in use a 
weave of four liarnesses called the crowfoot weave, which is some- 
times called a sateen or doeskin, but as the first and second threads 
run consecutively to the right, and the third and fourth run con- 
secutively to the left, it cannot be a sateen. A true sateen must 
in no instance have two threads running consecutively either to 
the left or to the right. 

Sateens generally have a warp-flush surface, which gives a 
soft and full appearance to the fabric and are used more or less 
in the construction of fancy figured goods and piece-dyed fabrics, 
such as damasks and table linen, covert coatings, beavers, etc. As 
the weave is either a warp-flush or a filling-flush face, the char- 
acter of the cloth is always of a limited nature. 

The derivatives of the sateen are very diversified in character, 
but more perfect in structure than those obtained from other weaves 
or modes of interweaving. 

So far, we have been considering simple weaves or cloths con- 
structed on a one-weave basis, but the method of constructing fabrics 
from a combination of several weaves, is a most comprehensive one 
and the effects produced cover a wide range of fabrics. 

Combination of Weaves. In all cases when a fancy figured 
effect is required in cloth made from the same shade of yarn, this 
principle is invariably adopted, as every plan of interweaving, 
whether twill, basket, diamond, herring-bone, spotted or all-over 
effects, can be produced by a combination of weaves. 

The essential points to be noticed in combining or amalgamat- 
ing two, three, or more weaves are («) class of fabrics to be con- 
structed, {})) the capabilities of each weave intended to be combined 
with other weaves. 

Some weaves are specially adapted for cotton effects, others 
for silk, woolen, or worsted. To combine weaves without due con- 
sideration as to their utility is a useless toil. To amalgamate 
weaves for fulled-woolen goods is a waste of time, as weaves for 
woolen goods should be of a regular and uniform character, and 
those nearly approaching each other are preferable. In cotton and 
worsted goods the opposite characteristics are desired, and the man- 



TEXTILE CALCULATIONS 



ner of interlacing is of the utmost importance; the principal feature 
of a worsted fabric being its decided and clearly defined weaves. 

Our considerations have thus far been the structure of a fabric 
as affected by the weave. For our next consideration we will take 
the structure of a fabric as affected by its relation to warp and filling. 
The strength^ ut'dtty^ and the j^urjjose of tlie structure must 
be considered. Generally speaking, the smaller the yarns, the 
larger the flushes in weaves which may be employed. A cloth con- 
structed with yarn 2,560 yards to the pound, 24 threads to the inch 
using the plain weave would be firm and regular in construction, 
but if it were woven in an 8 -harness twill, 4 up. and 4 down, it 
would be very loose, coarse and open in construction. This clearly 
shows that weaves that are useful for one class of yarn, are not 
suitable for all, so we must have in mind the quality of texture 
required, when laying out or constructing a cloth. 

When combining weaves the importance of the filling capacity 
must not be lost sight of, and when several weaves are combined, 
the complete design must possess a similar capacity for the ad- 
mission of the fillinDr. 

The construction of a cloth in its broadest sense is, to consider 
the weave, size of yarns and materials of which they are made, 
and also to enter into the details and calculations required in con- 
nection with the correct method of building a perfect structure. The 
following 2)01 at s should he noted ivhen constructing ci fahric : 

Weave, or combination of weaves. 

Judgment in selecting weaves for combination. 

The class of fabric intended to be produced, whether wool, 
worsted, cotton, or silk. 

The weaving capabilities of the separate weaves to be combined. 

Weaves combined to have an equal filling capacity. 

The purpose and utility of the fabric. 

INTature of the raw material to be used. 

The size of the yarns for warp and filling. 

The number of turns of twist to be put in warp and filling yarns. 

The number of threads in the warp per inch. 

The number of picks of filling per inch. 

The take-up in weaving. 

The process in dry finishing. 



40 TEXTILE CALCULATIONS 



JSc'ourino;, fiillintr shearino;. 
Finisliino; .shriiikao-e. 

DIAMETER OF THREADS. 

The square root of the yards per lb. will give the diameter of 
the yarn, or the number of threads which will lie side by side in 
one incli without being interlaced with another set of threads. 

Example. Suppose a cloth is to be made from 80's cotton, 
and it is desired to ascertain the number of threads that will lie 
side by side in one inch of space. 

80 X 840 = 67,200 yards of 80's cotton in 1 lb. Extract- 
ing the square root of 67,200 

V 67,200 = 259.22. 

Allow 7 per cent for shrinkage of yarn from first spin. 

259.22 - 7% = 241.07. 

Note. — When the tension, which is put on yam in spinning, is re- 
moved, cotton shrinks 7 per cent ; worsted 10 per cent ; woolen 14 per 
cent ; and silk 4 per cent. 

As a fraction, it will give the diameter of the thread, as g-J-y 
of an inch, therefore, 241 threads of 80's cotton would lie side by 
side in one-inch space. The same rule will apply to woolen and 
worsted yarns, where the basis of the calculations is of a similar 
character. 

Example. Suppose a cloth is wanted from 40's worsted. 
40 X 560 = 22,400 yards per lb. 
l/ 22,400 = 149.66 - 10% -= 134.70 (approximately 135.) 

Therefore 135 threads of 40's worsted will lie side by side in 1 inch. 
Rule 31. To find the diameter of any yarn use the square 
root of 1 counts in yarn required, as a constant number, and multiply 
the square root of the counts of the required diameter by the con- 
stant. Thus the square root of I's worsted is -j/ 50O = 23.66. 

23.66 - 10% = 21.30 
What is the diameter of 16's worsted yarn? 

p/^jj- == 4. 21.30 X 4 =- 85.20. 
F^roof. 560 X 16 = 8,960. 1/ 8 960 = 94.65 - 10% = 85.19. 



TEXTILE CALCULATIONS 41 

BALANCE OF CLOTH. 

There are no definite rules to determine what is perfection in \ 
a textile fabric The term "Balance of Cloth" is capable of wide 
interpretation, but the generally accepted meaning is the propor- 
tion in which the warp and filling stand to each other. A second 
interpretation is the distance the threads are set from each other 
according to their weight and diameter. This would be correct if 
all cloths were made on the same principles, but as all classes of 
fabrics are not made for the same purpose, either as to wear 
or general utility, no definite nor systematic rules can be given 
that will apply to every variety of textiles. 

Suppose a concern is making dress goods, and has found that 
the layout or construction of this fabric, on a plain weave basis, is 
all that can be desired. The warp and the filling threads are made 
of the same material, and the warp is so set in the reed that the 
diameter of the threads and the spaces hetween the threads are 
equal ^ the filling threads are equal in counts or diameter to the 
warp threads, and there are the same number of threads and spaces 
in the same area as there are in the warp. This layout may be 
considered as representing an equally balanced fabric, and it does 
not matter what the material may be, whether cotton, linen, woolen, 
or silk, the construction of such a cloth is perfect and is made on 
the truest principles. 

Taking the plain cloth as here laid out as the foundation for 
a reliable basis, we have something on which to commence our 
further studies on cloth construction. 

It very frequently happens that to produce special effects, this 
principle must be departed from. We may wish to make a cord 
or rib running in the direction of the warp, or we may wish the 
cord to run across the cloth in the direction of the filling. These 
two fabrics are made on two distinct principles, and although the 
variation in texture is due to alterations and modifications in the 
weave, the foundation of both is the plain weave. In the plain 
weave the threads are equal, both warp and filling being deflected, 
but in a corded effect, one set of threads is heavier than the other, 
which results in the light thread being bent and the heavy thread 
retaining its straightness. 

In such instances, there is no space between the warp threads 



42 TEXTILE CALCULATIONS 

for tlu^y may be in actual contact^ and the number of threads per 
inch determined by tlie diameter of the threads, without any allow- 
ance for space between them. Poplins are a good illustration of 
this construction. In this class of goods the cords run across the 
cloth, and instead of the warp threads having a space between them 
e(|ual to the diameter of the threads, they must be set very closely 
together, and the filling threads some distance apart, otherwise the 
clear cord will not be produced. Care must also be taken that 
the filling threads are not too far apart, or the corded effect will be 
destroyed. When producing a cord parallel to the length of the 
cloth the procedure is exactly the reverse. 

From these two examples we come to another conclusion, i.e.^ 
on the warp cord, the warp is present in larger quantities than 
the filling, while on the filling cord, the filling is the larger quantity. 
It has been stated that as the warp or filling preponderates, it 
must be increased in quantity, and that w^hich is least seen must 
be decreased. This rule holds good for nearly all makes of cloth. 

Twilled Cloths differ very much from plain fabrics. By the 
construction of the weave the threads must be closer together, for 
the same counts of warp and filling, to produce a cloth of equal 
firmness. A plain cloth is interwoven at every thread and pick 
whereas in a twill cloth, the picks pass over a number of threads 
before they- are interw^oven, therefore, weaves which produce long 
floats require heavier yarn or a closer set to produce an approximate 
firmness of texture. The number of threads and picks per inch 
must be increased in proportion to the length of the floats. 

In twilled cloths, the warp or filling may be made to pre- 
ponderate on the face of the fabric in two ways, («) as in plain cloth 
by having more threads of one set than of the other, at the same 
time decreasing the diameter of one set of threads, and increasing 
the diameter of the other, or {!)) by weaving the desired set of 
threads on the face. 

To Change From One Weave to Another and Retain the Same 
Perfection of Structure. As has been explained in regard to the 
plain fabric, w^hen it was desired to change from the plain weave 
to a fancy twill or diagonal, it may occur that one of these fancy 
twills may be desired in some other effect, and at the same time be 
necessary that no alteration of the structure of the fabric take place. 



TEXTILE CALCULATIONS 13 

A heavier or bolder twill may be desired, or it may be that the twill 
is too deep or prominent, or that a still lighter fabric is in demand. 
The layout or texture of the original fabric is known and it is re- 
quired to construct a new fabric of exactly the same character, and 
also to use the same size and quality of yarns as in the first clotli, 
thus saving the expense of making new yarns. For example, we 
have a cloth woven with the 4-harness cassimere twill, 80 threads 
per inch, warp and filling being equal. We now desire the same 
build of cloth, made from a design that will give a bolder twill, eo 
the 6-harness common twill -— is used. How many threads and 

picks per inch must be used in the new fabric? 

(«^) Obtain the number of threads and units in known weave. 

(h) Obtain the number of threads and units in required weave. 

[c) Obtain the number of threads and picks per inch in 
known fabric. (Threads and picks per inch is known as texture.) 

Rule 32. Multiply the number of known threads or texture 
by the units of the known weave, and by the threads of the required 
weave, and divide the product by threads of known weave, multiplied 
b}' the units of required weave. 

The term unit is given to the threads and intersections of a 
weave. For example, the plain weave has one thread up one 

thread down, expressed — ! L. Each pick of filling passes over 

threads 1, 3, 5, 7, etc.. and under threads 2, 4, 6, 8, etc., or vice 
versa, thus forming a space between every thread and those on 
either side. To find the number of units, the weave should be 

X I I 
expressed — — the crosses representing threads, and the vertical 

lines representing intersections. It will be seen that the plain 
weave contains two threads and two intersections, or four units. 
The cassimere twill would be two threads up and two threads 

XX I ! 

down, expressed ^ which shows four threads and two inter- 

I XX I 
sections, or six units. 

XXX I i 

The three up and three down twill would be ^ — ^ 

^ I XXX I 

or six threads and two intersections, or eight units. 

Proceeding with the problem given above 
Texture (80) X known weave units (6) X threadsof -required weave (6) _ 
Threads of known weave (4) x required weave units (8) ~" 



44 TEXTILE CALCULATIONS 

Thus 90 threads and picks per inch on a G-hariiess twill will ^ive 
the same texture as 80 threads and picks per inch on a cassiniere 
twill with the same counts of yarn. 

It is required to change from the weave, 2 up, 1 down, 1 up, 

2 down; to the weave 2 up, 1 down, 1 up, 1 down, 1 up, 4 down. 
The texture is 72 threads and 72 picks per inch. 

First w^eave has 6 threads and 4 intersections = 10 units. 
Second weave has 10 threads and 6 intersections = 10 units. 

72 X 10 X 10 ^_, , , . . . , 

-— = To threads and picks per inch. 

o X 10 ^ ^ 

If it is necessary to make the cloth lighter and maintain the 
structure of the heavier cloth, and to use the same yarn, a firmer 
weave must be used to reduce the number of threads per inch. 
Proceed in the following manner: 

(ct) Obtain the number of threads and units in known weave. 

(b) Obtain the number of threads and units in the required 
weave. 

(g) Obtain the texture of known weave by finding threads 
and picks per inch. 

Rule ^^, Multiply the known texture by the threads of the 
required weave and by the units of the known weave, and divide 
the product by the units of the required weave multiplied by the 
threads of knowm weave. 

If a fabric woven with the weave 3 up, 1 down, 1 up, 3 down, 

3 lip, 1 down, 1 up, 3 down, has 80 threads per inch, and we wish 
to use the weave 2 up, 1 down, 1 up, 2 down, 2 up, 1 down, 1 up, 
2 down, how many threads will be required to maintain the exact 
structure of the original cloth ? 

First weave has 16 threads and 8 intersections = 24 units. 
Second weave has 12 threads and 8 intersections = 20 units. 

Texture (80) X threads required weave (12) X units of known weave (24) 
Units of required weave (20) X threads of known weave (167) ^ '" 

Thus 72 threads per inch will give the same texture on the second 
weave that is produced by 80 threads per inch on the first weave; 
using same counts of yarn. 

In all these examples it is assumed that the warp and filling 
are equal in size, quality, and texture of the fabi'ic, and the fabric 



TEXTILE CALCULATIONS 45 

is built on the principle of what is generally understood as a 
square cloth. 

Having determined that a truly balanced cloth is where the 
number of threads and picks are equal and of the same diameter, 
and having determined what sett of reed will give the best result for 
a given number of yarn, it is easy to find what sett will suit any 
other count of yarn to produce a similar result. For example, we 
will take four threads of a plain cloth. 

X I \ ^ \ I ^ threads = 4 units. 

I X I I X I 4 intersections = 4 units. 

8 units. 
In a fixed rule, we assume that the proportions of size of yarn 
warp and filling, and spaces are equal, therefore w^e will take the 
diameter or size of yarn as the unit of measurement. Supposing 
our sample of plain cloth to have 60 threads per inch, and we wish 
to change the weave to the 4-harness cassimere twill. 

XX I I 4 threads = 4 units. 

I XX I 2 intersections ^ 2 units. 

6 units. 

Four threads of plain cloth equal 8 units, while the same 
number of threads of the cassimere twill equals 6 units, therefore 
the twill weave will require a greater number of threads to make 
as perfect a fabric as the plain weave, and the increase is in pro- 
portion as 6 is to 8. Our example supposed the plain cloth to have 
60 threads per inch, then to have an equal fabric with the twill 
weave, the problem will be 6 : 8 :: 60: X or 80 threads per inch. 

As the cloth is built square, what has been said of the warp 
applies equally to the filling. The 4-harness cassimere twill inter- 
weaves regularly, the twill moving from end to end consecutively. 
Warp and filling flushes are equal, as in the plain weave, and the 
quantities of warp and filling on the face are equal. 

Take another example — 5-harness twill, 3 up and 2 down. 

XXX I I 5 threads = 5 units. 

I XX I 2 intersections = 2 units. 

7 units. 

Two repeats of the weave wouia equal 14 units. Ten threads 



46 TEXTILE CALCULATIONS 

of the plain weave would equal 20 units, therefore the 5-harness 
twill requires a (jreater nuinher of threads. 

The increase is in proportion as 14 : 20 :: 60: X or 85 ^-Yg-. 
We will take a final example on the G-harness common twill 
basis, three threads up and three threads down, the filling passing 
over and under three threads alternately, therefore there will be only 
2 intersections; xxx | ooo | =: 6 threads and 2 intersections equals 
8 units. In a plain weave, there would be 6 threads and 6 inter- 
sections, equaling 12 units, so this weave would require an increase 
as 8 : 12 :: 60 : X which equals 90 threads. 

It must be thoroughly understood that the examples given' 
herewith are all supposed to be made from the same material, same 
kind of yarn in weight and diameter, and the structure of the fabrics 
is exactly the sam6 as far as the build is concerned, but as the 4, 
5, and 6-harness weaves require more threads per inch to form as 
perfect a structure as the plain weave, the fabric when woven must 
necessarily be heavier. This is one of the important considerations 
when laying out a new fabric. The weight per yard has to be taken 
into account, therefore the size of yarn and weave are two very 
important factors. 

In order to make proper use of previous calculations, and to 
put them into practice, it is necessary that the actual size of threads 
should be known, that is, the size, counts, and diameter to produce 
a perfect structure. Threads composed of different substances vary 
greatly in proportion to their weight. The specific gravity of cot- 
ton and linen is about 1 J times the weight of water. Animal fibers, 
silk and wool, have a specific gravity of 1 ^^-^ or nearly 1^. 

The diameters of linen threads are similar to cotton. Woolen 
yarns present a thicker thread for the same weight. Spun silk has 
about the same diameter as cotton. 

We must now consider the diameter of yarns. Threads vary 
as to the square root of their counts. After finding the diameter 
of a thread, find how many threads will lie side by side in one inch. 
For any counts of yarn, find the number of yards per pound and 
extract the square root. The square root of number 1 cotton w^ould 
be v'' 840 = 28.98. This is without any allowance for shrink, 
age, and without any allowance for space. 



TEXTILE CALCULATIONS 47 

Rule 34. To change a plain weave into a fancy twill or 
diagonal and retain the same perfection of structure: 

((f) Obtain the number of threads in required weave. 

(Jj) Obtain the number of intersections in required weave. 

(r) Add threads and intersections together and call them units. 

{(T) Obtain the units there would be in the number of 
threads of the plain weave that are occupied by the required 
weave. 

Example. If a plain fabric has 80 threads per inch, what 
number of threads will it require for the weave 3 up, 3 down, 2 
up, 1 down ? 

^Multiply the units of the known weave by the threads per 
inch, and divide by the units of the required weave. 

Explanation. In two patterns of the above weave, there would 
be 18 threads and 8 intersections = 26 units, a plain weave on 18 
threads would have 18 intersections = 36 units. 
26 : 36 :: 80 : X = HO-iVV 
Thus 110 threads will be required to produce a fabric on the re- 
quired weave, which is equal in texture to 80 threads on a plain 
weave; the same yarn being used in each case. 

DISSECTING AND ANALYZING. 

In the manufacture of textile fabrics, there are at least two 
important divisions of a designer's work: (a) designing, (Ij) dis- 
secting and analyzing. 

Designing consists in the building of a fabric from designs, 
more or less original, and the weaves, texture of the fabric, and 
colors used in its manufacture are limited only by the looms and 
yarns under the designer's control. 

Dissecting and Analyzing differs widely from designing and 
is the most important w^ork in a design office. In this case the 
designer must reproduce or imitate a fabric; which is a difficult 
problem if not worked in the right way. A thorough knowledge 
of designing in all its branches, and a theory of the many calcula- 
tions necessary, together with the most expedient manner in which 
the theory may be put into practical use are essential for a suc- 
cessful analysis. 

Many designers perform their work without any special meth- 



4S TEXTILE CALCULATIONS 



od, which causes great inconvenience to themselves, and results in 
a useless waste of time and material. A methodical designer can 
perform his work in a comparatively short time with far better re- 
sults, saving the manufacturer considerable time and expense. The 
first princi])le of a designer should be laethod^ for method leads to 
economy, which is one of the foundations of a mill-man's success. 
Too much stress cannot be laid upon this point, and if the begin- 
ner is methodical and continues so, dissecting and analyzing will 
prove comparatively easy to him. 

When analyzing a fabric, many important facts must be con- 
sidered, especially when it is desired to reproduce the fabric. The 
nature of the fiber from which the yarn is spun, the quality and 
twist of the yarn, colors, and weaves used to produce the desired 
effect, and the character of the finishing processes should all be 
carefully studied, in order that the reproduction may be perfect in 
every detail. 

The first thing to determine is the class and nature of the 
fahric. Double, triple, and backed cloths may be easily determined 
by a close inspection of the sample, one side usually being woven 
with coarser yarn than the other. Heavily napped fabrics should 
first be singed, care being taken to singe the nap without injuring 
the yarn in any way; while single cloths need but a glance to 
classify them as such. 

The next step is to decide upon the face and the back of the 
fabric. Double and triple cloths usually are woven with a heavier 
yarn on the hack to add weight and strength to the material. This 
is especially true of the so-called "two and one" system. Fre- 
quently "one and one" cloths are woven with yarn of equal counts, 
and the face is determined only by one or more of the several tests 
described later. The conditions which apply to double cloths also 
apply to backed cloths. 

AVorsted dress goods and similar fabrics often prove confus- 
ing, but in many cases a close examination will show that one side 
is smoother to the touch than the other, and the "draw" is very 
noticeable. By passing the fingers one way of the cloth a smooth 
feeling is noticeable and this is termed the "draw". Passing the 
fingers the other way of the cloth a slight resistance is felt, which 
is termed the "bite". These conditions are caused by shearing. 



TEXTILE CALCULATIONS 49 

and are undoubtedly the best test for the determination of face 
and back. Union goods are usually woven with the animal Hbres 
more prominent on the face. 

The next thing to consider is the scheme of warp and lilling, 
and the texture of the fabric, and is practically the first step in 
dissecting. 

Every woven fabric is composed of two sets of threads or yarns. 
Those runninof lengthwise in the fabric or in the direction of tlic 
warp are commonly termed threads, while those running across the 
fabric, or in the direction of the filling or weft, are termed the picks. 
From now on, the terms threads and picks will be used to denote 
warp and filling respectively. 

We are now confronted by the problem of determining which 
is warp and which is filling. If the sample contains a portion of 
the selvedge there is no difficulty, for the selvedge always runs in the 
direction of the warp. If, however, the sample is cut so that no 
portion of the selvedge is present the warp may be determined by 
any of the following tests: 

(a) If the yarn is double and twisted one way and single the 
other, the double and twisted yarn will indicate the warp. 

Qj) If the yarn is harder twisted one way than the other, the 
yarn with the harder twist is the warp. 

(c) If one set of yarn is finer than the other, it is safe to say 
that the finer yarn forms the warp. Usually yarn used for warp 
is finer than that used for filling. 

{d) If the yarn one way appears straight and regular, and 
the other way loose, rough, and displaced, or not strictly regular, 
the straight yarn is assumed to be the warp. 

(e) Reed marks of any kind will show which is the warp. 

(y) If the yarn one way is single or double cotton, and the 
other way is single woolen, the cotton is invariably the warp. 

[(j) If the yarn one way is starched or sized, and the other 
is not, the starched yarn is the warp. Warps are sized or starched 
to add strength or weight to the yarn. 

(K) The test for nap has been previously stated and is valu- 
able to denote the warp, for the nap lies in the direction of the warp. 

(%) Stripes are generally formed by the warp. 

Q*) A fabric may be woven with the yarn right twist one way 



\mJ^ 



no TRXTTLE CALCULATIONS 

and- yarn left twisl tlic otlicr way. The toi-iiici- is iiivariahly tlie 
warp. 

Exceptions to these tests seldom occur. In many fal>rics. 
varying conditions prevail, but the reasons for such variations are 
so pronounced, especially with yarn, tliat little examination is re- 
quired to distinguish the warp from the filling. 

Warp yarn is usually stronger and finer than filling yarn, 
with a harder twist, and made from the best and strongest material 
on hand. 

Texture. The density of a fabric is controlled by the texture, 
and its required weight and thickness. The sample should be cut 
to a certain size, usually 1 inch square, and each thread drawn out 
of the fabric separately and laid aside in its proper order. Each 
thread should be examined in turn, and the t/vist, nature, and 
colo/' determined as it is drawn out of the sample. This will save 
a repetition of the work later on. When only a small sample is 
available the texture and color scheme must necessarily be deter- 
mined at the same time. 

Having drawn out each set of yarn, warp, and filling, the tex- 
ture may be ascertained by counting the number of threads in each 
lot. If in the sample on hand there are 56 threads in the w^arp 
and 48 threads in the filling;, the texture w^ill be 56 threads and 48 
picks per inch. It is not always convenient to cut the sample 1 
inch square, and the threads and picks per inch may be determined 
by accurately measuring the length and width of the sample, and 
dividing the picks and threads respectively by these measurements. 
A sample may be |-inch long and li inches wide and contain 36 
and 84 threads respectively. The calculations would be 
36 H- I =48 picks per inch. 
84 -r- li = 56 threads per inch. 

Note. — This is not a reliable method and, if possible, should be 
avoided o 

As the threads are drawn out, care should be taken to find 

the number of each variety and color of yarn, and in their exact 

order. When a repeat has been found by adding the number of 

threads of each color and variety, the threads in a pattern are 

determined. Suppose the threads in a sample are as follows: 



TEXTILE CALCULATIONS 51 

Twist cotton 2 2=4 

White worsted 2 =2 

Green worsted 2=2 

Thus there are 8 threads in a pattern, 4 twist cotton, 2 white 
worsted, 2 green worsted. 

Fabrics, such as plaids, frequently have a fancy arrangement 
of warp and filling, and the threads in a pattern exceed in number 
the threads and picks per inch. Determine the extent of the repeat 
in the sample and measure it accurately. By dividing the num- 
ber of threads in a pattern by the number of inches the pattern 
occupies, the texture may be found. Thus, a pattern 2 J inches 
wide contains 

Red cotton 18 = 18 

Blue cotton 36 = 36 

Yellow cotton • 4 ' =4 

Dark tan 54 =54 

White 48 = 48 

Light tan 80 = 80 

240" 
240 ^- 2.5 = 96 threads per inch. 

The easiest way to ascertain the woven construction of a fabric, 
is to take it from the face or from the figure presented on the sur- 
face of the fabric; but this requires experience and familiarity 
with the many kinds of weaves. Constant practice in constructing 
cloths from designs, and noticing the woven effects of each partic- 
ular '^sign''\ ''^riser''\ or ''sinker^'' used on the point or design 
paper is the best way to become familiar with weaves. But some- 
times, the sinkers and risers are so intermingled, several individu- 
alities being contorted and merged into one eccentric combination, 
that even experts find it necessary to resort to unravelling or 
''picJcing-out'''* each warp and filling thread, in order to find the 
true character ot the weave. 

The picking out of samples presents no difiiculties except 
those of concentrated sight and steady application. This only re- 
fers, however, to fast-woven and much felted cloths, in which all 
the crossings have become nearly, if not totally, obliterated. If 
the texture were as open as mosquito netting, there would be no 



52 



TEXTILE CALCULATIONS 



difficulty, because every crossing of the threads, warp, and filling 
could be distinctly seen and marked. 

Of course there are gradations from the most openly constructed 
to the finest setted fabrics, and from the least to the most heavily 
felted cloths; still the principle of dissection is the same in all. 

There are other particulars to be obtained from a sample, 
besides the weave or figure, and upon which the figure depends for 
its appearance. These are the relative fineness of the warp and 
filling, and the number of threads per inch, and also the amount 
and kind of finish to be given to the fabric to gain solidity and 
handle, as well as effect. We say nothing here of the materials 
of which the threads are composed. 




15*?^- 3^: m w m »« >K >« w-j 
iVKWm. :—: j*c «€ >i« »« i*e 3*t a*« ; 

^J« 3*1 »£ SIC 3*1 »« 3«C 3*C 3tU« 
^ 3«C 340C I4C i#C }tC>#C MC 3*C : 

:*t JK MC 3«£ MC 3K 3« W i*C»^ 

■■<m 5it 3*e Mc 3*c 5fe: 3*e m£J**»^ 
„ /*e »e 3« 3#c 3+c :«: :*c i« 3«J« : 
g;. 5«c 3*e Mc s«c 3m: y^-^ »*<*•« ^ 
Z^, 5*r M 3M 3*c -A! j^: :m ^#€ >c ■• 



Fig. 5. 

Now, suppose a sample of finished cloth exactly 1 inch square 
is to be analyzed. The first procedure is to weigh it in very fine 
(grain) scales, and record the weight. Assuming that the weight 
of one square inch is 5 grains and that the finished cloth is 56 
inches wide, we proceed to find the weight of one yard of cloth. 

Rule 35. To find the weight of 1 yard of cloth, weight of 
1 square inch and v/idth being known. Multiply the grains per inch 
by the given width of cloth X 36, and divide by 437.5 grains. The 
answer will be weight in ounces per yard. 

5 X 56 X 36 

— — = 26.04: ozs. per yard. 



TEXTILE CALCULATIONS 



53 



Or the constant found by dividing 437.5 by 36 may be used as 
follows : 

5 X 56 -^ 12.153 = 23.04 ozs. per yard. 

Note. — The weight of woven fabrics is usually expressed in ounces, and 
as there are 7,000 grains in one pound] Avoirdupois, 7,000 ^ 16 = 437.5 grains 
per ounce. 

Rule 36. To find the weight of one yard of cloth when the 

weight of any number of square inches is known; weight in grains 

of sample X width X length, divided by square inches X 437.5 

grains. 



« ,^i .rfSF 



iWPt .#WL JW» J'HL -JWfc .J*!^ PPC JNpL 

3«C M< 1«C SW NC 3W J9C hI)^ 
e *^ :^ MC Ml MC WC )«C MC ^ 
3i«: ^: 39C MC M M MC |«<M 
( i^: -^ M£ MC MC 3«C MC IM ; 



:«3#e.j«SKj«Ci 



Assuming that a sample which contains 4 square inches weighs 

20 grains and the cloth is 56 inches wide the process would be as 

follows : 

20 X 56 X 36 

- — . . .3>y ^ — = ^0.04 ounces per yard. 

The above explains the general principles which underlie the 
"method of obtaining the weight per yard of any fabric, woolen, 
worsted, cotton, linen, or silk, of any given width, and should be 
thoroughly understood by all who are employed in the designing 
room, weave rooms, or in the superintendent's or 'manager's otfice. 

This simple formula with explanations will apply to all fabrics. 

Grains X width X 36" 

-. — r ^^ ^Q>7 K — — ounces per yard. 

sq. inches X 437.5 ^ "^ 



r>4 



TEXTILE CALCULATIONS 



PICKINQ-OUT. 

[(f) Trim the edges of the sample perfectly square with the 
warp and filling threads. (See Fig. 5.) 

(^) Unravel, by taking out about one-quarter of an inch of 
warp threads from the left side of the sample and about one-quarter 
of an inch of filling threads from the bottom part of the sample. 
(See Figs. 6 and 7.) 

(^') Take the sample in the left hand between the finger and 
the thumb, placing the warp threads in a vertical position, that is, 
the first thread of weave on the left and first pick of weave nearest 
your body. 




ij^^^' !^C^ J^C J^C Jm% J^ Jilif -'^^- 

•-**^''*** •>•** ^■^'* **« «^.*r ■ 



Fig. 7. 

A piece of design paper must be at hand to mark down the 
result of the pick-out, as shown in the diagrams. With a small 
pointed instrument, say a needle, commence at the left hand lot- 
torn corner and lift the first thread away from the body of the cloth 
so that the filling crossing can be seen. 

Now notice which filling threads this firsi thread is over and 
under, and mark on the design paper (commencing at the left hand 
bottom corner) those picks which are down ; the up picks, of course, 
will be represented by the blanks or vacant squares. For instance, 



TEXTILE CALCULATIONS 





Ix l> id 


y J xl b 




I P*P 




] M) 




X 1 <[ p 


<] « pi 


Ot Ixj 


bo > xl 


X witxT 


Mx wA( 


1 wod 


1 IxDOa 


A P'rp 


■■ Xp 


7 1 ^jl 


^l> 


1^1 


■■ ~ 




^a 






3 iB^T^T 


■■ IxtW 


z l^^ko_i 


[g^Sp 







ABCDEFGM 

Fig. 8. 



the first warp thread is over the lirst and second picks, under the 
third pick, over the fourth pick, under the fifth pick and sixth 
pick, over the seventh pick, and under the eighth pick: that is.^ 
over two, under one, over one, under two, over one and under one. 
The ninth and tenth are like the first and second, the eleventh is 
like the third and so on; so the first eight picks 
represent one repeat of the weave on the first 
thread, and is represented on the design paper by 
the black filled -in squares on thread A, Fig. 8. 

Now remove the first thread, lift the second 
thread to the front, and proceed as before. The 
second thread is over the first 3 picks under 4 
over 4 and so on as shown at the thread marked 
B. Each succeeding thread is treated in the same manner until 
the weave or design repeats. 

When the pattern is found to be repeating in either direction, 
the pick-out need not be continued, yet for safety it is advisable 
to go far enough both ways and then fill in the design at the repeats 
and disreo^ard the other crosses. This design is com- 
plete on 8 threads and 8 picks, as shown at Fig. 9. 

Fig. 9 also shows the dra wing-in draft and 
harness chain. The design is reduced to four har- 
nesses to work it easily. The letters above the 
drawing-in draft correspond with those in Fig. 8 
and denote the order of the threads and the order of 
their drawing-in upon the harness, and the figures 
under the draft the number of the harness upon 
which each thread must be drawn, according to the clJ SWF^ 3 
design, while those on the left hand side show the ' T^~^^ 

O ' S7654.32I 

number of harnesses employed. The numbers on ^^^ness chain 
the left of the reduced chain show the condensation ^^* 

of the design and draft. Fig. 10 shows the interweaving of the 
threads. 

However intricate the sample or design may be in its woven 
construction, this method will simplify it. Sometimes the design 
will not repeat on so small a number as 8 X 8, and if the sample 
is not large enough to obtain one-half repeat, a larger sample must 
be obtained if possible, unless it is seen that the design runs in 



ABODE FGH 




FULL DESIGN 
ABODE FGH 



I 22 13443 
DRAWING-IN 
DRAFT 



TEXTILE CALCULATIONS 




recTular order, wlieii a few threads taken out are sufficient to show 
the principle of construction without going further. 

With constant practice in the analysis or picking-out of 
samples, the character of the figure or weave may be ascertained 
almost as well as in its production in the loom, as in both cases 
one becomes familiar with signs, sinkers, and risers and their effects. 
The preceding remarks have had reference to comparatively 
easy and simple textures for analysis, such as worsted or cotton 
goods, but with the more heavily felted 
woolen fabrics a little preparation is neces- 
sary before proceeding with the above meth- 
od. Any fibers which obstruct the clearness 
of the design and prevent the interweaving 
of the threads from being clearly seen must 
be removed by singeing or shaving the sur- 
a*b'c D*E> GH face; care being taken that the threads are 
Fig. 10. j^Qi destroyed, or damaged so that they can- 

not be removed, or followed in their regular course. 

Pattern. Having found the construction of the weave, so far 
as figure or design is concerned, the next procedure is to note the 
number of threads which complete the pattern in each direction. 

Referring to Fig. 11, the analysis of which is given on the 
analysis sheet, it will be noticed that the scheme or pattern of 
warp is, 2 threads of light, 1 thread of dark, 2 threads of light and 
2 threads of dark, or 

Light 2 2=4 
Dark 1 3 = 3 

7 threads in pattern, or scheme of warp. 
The pattern or scheme of the filling is 3 picks of dark and Z 
picks of light, or 

Dark 3 =3 
Light 2=2 

5 picks in pattern, or scheme of filling. 
Referring again to the analysis sheet for data the analysis is 
as follows: 

1. Weight of 1 yard, given width. 

Note. — Pattern refers to color only, design or figure refers to weave. 
In the first example the warp is dark and the filling light, which is termed 
solid colors. Pattern is the arrangement of colors as they lie side by side in 
the warp and filling. 



TEXTILE CALCULATIONS ' 57 



SAMPLE CLOTH ANALYSIS. 

The analysis or dissection of a sample of cloth consists in ob- 
taining the following particulars: 

Fabric Worsted Dress Goods (See Fig. 11) 

Data One square inch weighs 1.7 grains 

Threads per inch (finished cloth) sa. ..weigh.. ..9 grains 

Picks per inch (finished cloth) 50. . . weigh — 8 grains 

Width within selvedges (finished) 36 inches 

Remarks 56 threads per inch equal 56 inches of ivorsted yarn 

50 picks per inch equal 50 inches of worsted yarn 

1. Weight of one yard inside selvedges (1.7 X36X H6) -^ 437.5 = .5.0.9 ozs. per yd. 

2. Pick-out See Fig. 12 

3. Drawing-in draft and chain See Fig. 12 

4. System or dressing of warp, 

Light 2 2 =4 ^ 



.Dark 1 2=3. 

7 



5. System or scheme of filling 

Dark 3 = 5 . 

Light . 2=2 



6. Threads in warp 36" X 56 = 2016 ends 

7. Threads in warp pattern 7 

8. Patterns in warp, 2016 -^ 7 = 288 

10. Size (counts or run) of warp in finished cloth 

{56 X 7000) ~ (.9 X 560 X 36) — 21.6 loorsted counts 

11. Size (counts or run) of filling in fi.nished cloth. 

(50 X 7000) -r- (.8 X 560 X 36) = 21.7 worsted counts 

Note. These counts represent the yarn just as it lies in the sample 

It is not stretched 

11. Weight of warp yarn in one yard of finished cloth. 

.. Light 288 X 4 =1152 

Dark 288 X 3 = 864. . . . (2016 X 16) -^ (21.6 X 560) = 2.66 ozs. 

2016 

12. Weight of filling yarn in one yard of finished cloth 

36X50= 1800. . . . (1800 X 16) -^ (21.7 X 560) = 2.37 OZS. . 

2.66 + 2.37 = 5.03 OZS. per yard 



58* 



TEXTILE CALCULATIONS 



Grains 



A Wl 



dth X 36 



487.5 



— 5.08 ozs. weight per yard. 



2 and 8. Pick-out, drawing-in draft and chain (see Fig. 12.) 

4. System or pattern of warp according as the colors lie side 
by side in the fabric. (See Page 56.) 

5. System or pattern of filling, according as the colors lie 
side by side in the fabric. (See Page 56.) 

6. Threads in warp. Width (36) X threads per inch (56) 
-- 2.016. 




Fig. 11. 

7. See Ko. 4 for warp and No. 5 for filling. 

8. Patterns in warp. Threads in warp (2,016) ^- threads 
in pattern (7) = patterns (288). 

9. Size (counts or run) of warp in finished cloth 21.6. 

Note. — See rules for the various ways of obtaining counts from small 
quantities or short lengths of yarn. 

10. Size (counts or run) of filling in finished cloth 21.7. 

11. Weight of warp yarn in one yard of finished cloth. Width 
of goods (36") multiplied by threads of warp per inch (56) gives 
the total number of yards of warp yarn in one yard of goods, or 



TEXTILE CALCULATIONS 59 

2,016 yards. As the warp yarn is numbered 21.6, or as it takes 
21.6 times 560 yards to equal 1 pound of yarn, the weight of above 

2,016 yards would be ~ = lbs., or multiplied by 16 = 

^ 21.6 X 500 ' 1 ^ 

2.66 oz. of warp yarn in one yard of cloth. 

12. Weight of filling yarn in one yard of cloth. The picks 
of filling per inch (50) times width of cloth {Si)) gives the length 
in inches of filling in one running inch of the cloth or 1,800 inches- 
Multiplying this amount by 36 inches gives the number of inches 
of filling in one running yard of cloth. Again dividing by 36 
inches, reduces it to yards. 

1,800 X 36 

7^ = 1,800 runnino; yards of fillincr in one yard of cloth. 

Note. — As multiplying and dividing by 36 would be superfluous, it is 
omitted from the form-ula. 

Following our reasoning in the explanation given in a previous 



Pick-out Drawing-in Draft Chain 

Fig. 12. 

paragraph, counts of filling X 560 yards gives the number of 
yards in 1 pound of filling, therefore, 

— I = lbs., or multiplied by 16 = 2.37 ounces, filling 

21.7 X 560 ^ -^ . ' & 

yarn in one yard of cloth. 

Weight of warp yarn in one yard = 2.66 

Weight of filling yarn in one yard = 2.37 

Weight of yarn in one yard 5.03 ozs. 

The weight of yarn in one yard should equal the weight of 
finished cloth jyer yard. 

Take=up. So far the analysis has been simply as the yarn 
stood in the cloth. Yarn in a finished piece of cloth must have 
more or less crimps or corrugations in it according to the weave or 
design used. 

The plain w^eave which interlaces at every thread and pick will 
require a longer warp than the 4-harness swansdown weave, to pro- 
duce a fabric of equal length, provided all other things are equal. 



60 TEXTILE CALCULATIONS 

This is a very important point in the analysis of any 
fabric. It must be remembered that a yard of yarn will itot 
weave a yard of cloth ^ so cloth is always shorter than the original 
length of warp from which it was woven, which is due to the take- 
up by its being bent around the tilling. 

The cloth is always narro'wer than the loidth the warp was 
spread in the reed previous to being woven, which is due to the 
tilling pulling in the edges of the cloth and to the tilling bending 
around the warp threads. It is a well-known fact, that cloth from 
two looms working side by side may vary in width and length, 
and each loom working apparently under same conditions. 

The material of which yarn is made and the manner in which 
it is spun, dressed, and manipulated in the loom, has much to do 
with the take-up in the weaving and finishing processes. The 
finer the quality of the filling and the softer it is spun, as compared 
with the warp, the greater take-up there will be in the w^idth. In- 
creased tension on the warp increases the length of the cloth, and 
makes the width narrower, up to a certain limit. If the filling is 
hard twisted and of a coarse nature, or coarser than the warp, the 
cloth will not take up much in the width. 

The warp for plain stripes and sateen stripes should not be 
placed on the same beam nor reeded in the same manper, as the 
plain weave will take up much faster than the sateen portion. Care 
should be taken in reeding weaves of variable intersections. 

The difference in temperature, weather, system of sizing, kind 
of loom used, tension of warp, tension of filling, also number of 
reed and picks per inch as compared with each other will affect the 
amount of take-up. 

The yarns in weaves of the rib and cord type, where three, 
four, or more threads or picks work together, act like heavy yarns 
and tend to retain a straight line, the finer yarns bending around 
them, consequently the fine yarns have the greater take-up. 

Rules may be given which will give good results and which 
have been proved to be practical, to some extent, for finding the 
various items necessary for the reproduction of a fabric, yet they 
are only approximately so, the best results being obtained by ex- 
perience and using the records of other fabrics. 

Note.— Take-up will be further explained under the heading " Take-up 
and Shrinkage ". 



TEXTILE CALCULATIONS fit 



SETTS AND REEDS. 

Having found the weave, draft, chain and counts of yarn as 
they appear in the finished fabric, the next important step is to 
find the ''sett" in loom, which inchides reed, dents per inch, 
threads per dent, approximate counts of the warp and filling yarns 
previous to being woven, and finally the picks per inch in loom. 

The density of the warp threads in the process of weaving and 
subsequently in the woven fabric, is represented by the relative 
number of heddles on the harness shafts, and the dents in the reed 
distributed over a fixed unit of space, which will include the num- 
ber of warp threads passed through each dent in the reed. 

The system of numbering reeds now almost universal in all 
the textile industries (perhaps with the exception of silk) is known 
as the ^Hhreads jper inch^'^ system. The number of dents per inch 
in the reed with two threads in each dent is the basis of the sett. 
If the reed has 40 dents per inch it is called a 40's reed or 80's sett. 
40 reed X 2 threads = 80 threads per inch. 

Obviously, the "dents per inch" is the simplest basis for a 
sett system and should be adopted w^here English measurements 
are used. 

For all reed calculations in this work, one inch is given as the 
unit of measurement, and the number of warp threads contained 
in that space, forms the basis of the sett. When the threads per 
inch are of an equal number, the reed for the divisions is easily 
found, that is for ordinary requirements. For instance, if 40 
threads per inch are required, a 20's reed 2, lO's reed 4, or 8's reed 
5 may be employed; that is, a reed having 20 dents, 10 dents, or 
5 dents per inch, each dent containing 2, 4, or 5 threads respectively. 

By this method the number of threads for the whole warp is 
easily ascertained as follows: A warp is required to be 70 inches 
wide, with 40 threads per inch, then 70 X 40 = 2,800 threads are 
required for the w^arp. 

A cloth has to be woven in a lOO's sett, 4 threads in each 
dent. How many dents per inch must the reed contain ? 
Sett -^ threads in dent = Reed. 
100 -f- 4 = 25 

A cotton fabric is woven 3 threads in a dent, 42 inches wide, and 



62 TEXTILE CALCULATIONS 

warp contains 2,520 threads. What is the sett and what is the reed ? 
Warp threads (2,520) -^ width (42) -= sett (60) 
Sett (60) -V- threads (3) = reed (20) 
A reed contains 1,320 dents in 33 inches, 2 threads in each dent. 
What is the reed ? 

Dents (1,320) 
Inches (33) X Threads (2) - ^^ '^^^• 
Given 120 threads per inch, to be laid 72 inches wide in loom. 
How many threads in warp? Threads per inch (120) X width 
(72) = threads in warp (8,640). 

Unevenly Reeded Fabrics. The requirements of design and 
the construction of the cloth are so various as to sizes of yarn, and 
the number of threads per inch employed in the warp, that the 
number of dents per inch in the reed is dependent upon it. But 
the number of threads m each division of the reed is not always 
uniform, that is, not always the same number in each dent through- 
out the whole width of the warp, this depending upon the pattern 
to be woven. For example, in the production of a fancy sateen 
stripe while 2 threads in each dent may be required, say for J-inch 
space, the following dents may require 3, 4, 5, or 6 threads in 
them, and then repeat w4th 2's and so on through the width of the 
reed. This will show that no hard and fast rule can be laid down 
which will cover every requirement. 

Example. A worsted stripe is made in which the warp con- 
tains 1,920 threads; it is laid 40 inches wide in the reed, and reeded 
as given below. Find the average number of threads per inch, 
and the number of reed. 
Pattern 1 dent =^ 4 threads black. 

1 " =4 " white. 

1 '' =: 6 " black. 

1 '' = 4 " white. 

1 'i = 4 " black. 

1 " == 2 " white. 

6 dents 24 " in pattern. 
Rule 37, To find average threads per dent, and reed for cloth, 
number of threads per dent varying. First find the number of 
threads in one pattern and the number of dents which they occupy, 



1,920 


-=- 


24 


= 


80 patterns. 


80 


X 


6 


= 


480 dents. 


480 


^- 


40 


= 


12 reed. 


1,920 


-=- 


40" 


= 


48 average. 


48 


-^ 


12 


:^ 


4 average 
in each dent. 



TEXTILE CALCULATIONS 63 

then divide the total niiinber of threads in the warp (1,920) by the 
number of threads in the pattern (24:) which gives the number of 
patterns in the warp (80), this multiplied by the dents in a pat- 
tern (6) gives the total number of dents required to reed the warp 
(inside selvedges). The number of dents (480) divided by the 
width of the cloth (40) gives the number of reed (12). Dividing 
the threads in the warp (1,920) by the width of the cloth (40) gives 
the average threads per inch (48), and dividing this by the reed 
(12) gives the average threads in each dent. Dividing the num- 
ber of threads in a pattern (24) by the dents in a pattern (6)*w^ill 
also mve tlie average number of threads in each dent. 

A fabric is made with 3,264 threads in the warp; set 40 inches 
wide in the reed, and is reeded as given below. Find the number 
of dents per inch in the reed. 

30 threads 2 in a dent = 15 dents 



20 '^ 1 " 


u 




= 20 


12 " 2 ^' 


ii 




= 6 


^liss one dent " 


u 




= 1 


12 threads 2 /• 


u 




= 6 


^liss one dent '' 


ii 




= 1 


12 threads 2 " 


ii 




= 6 


20 '' 1 '' 


u 




= 20 


30 '• 2 " 


ii 




= 15 



136 threads in 1 pattern. 90 dents in 1 pattern. 
3,264 ^ 136 = 24 patterns. 

24 X 90 =: 2,160 dents. 
2,160 ^ 40 = 54 reed. 
A cotton sateen stripe fabric has 3,520 threads in the warp and 
is reeded in a 40's reed as given below. What is the width in reed'^ 

22 threads white ] 

6 " It. blue ( ^ 
6 " '' pink r 2 in dent. . 

6 " " blue J 

12 " white ] 

12 '' It. blue I 

12 " " straw J- 6 in dent. 

• 12 " " blue I 

12 " white 



64 TEXTILE CALCULATIONS 



4 


u 


pink 


1 






4 


(( 


blue 


1 






4 


a 


)ink 


h 


2 


in dent. 


4 


u 


)lue 








4 


u 


pink. 








12 


Ik 


white 


1 






12 


- 


It. blue 








12 


u 


" straw 


^ 


6 


in dent. 


12 


u 


" blue 


1 






12 


u 


white 


J 






G 


^» 


It. blue 


^1 






6 
6 




" pink 
" blue 


1 


2 


in dent. 


22 


u 


white 


1 







TAKE=UP AND SHRINKAGE. 

Cotton Cloth. In cotton cloth, the take-up depends chiefly 
upon the character of the weave, and quality and counts of yarn 
used. The term "sley" is used to denote the number of threads 
per inch in the cloth. 

Suppose we have analyzed a cotton sample, and there are 100 
threads per inch, or 100 sley. Find the number of dents per inch 
in the reed to give this texture, using 2 threads in 1 dent. 

Deduct 1 from the given sley and divide by 2.1. 

100 - 1 := 99. 99 ^ 2.1 = 47.14 reed. 

As an illustration of how cotton cloths will vary in the amount 
of take-up according to the construction in weaving, the following 
examples are given: 

1. A fabric made with 48's warp and 2-15's filling, 34 inches 
in reed, 88 threads per inch, 50 picks per inch, 5 harness sateen 
weave, gives 38^ inches of cloth. Showing a take-up of about 
11 per cent. 34*^- 33.5 = .5. .5 ^ 33.5 = .0148 or 1.48%. 

2. 48's warp and 15's filling. 33 inches in loom, 64 threads 

by 40 picks. 5-harness — _- weave, gives 32 inches of cloth, 

showing a take-up of 3J per cent or 33 - 32 = 1. 1 -^ 32 = 
.03125 or 3^ per cent. 

3. 2-20's warp and 48's filling. 31J inches in loom. 48 
threads by 128 picks. 6-harness broken twill, filling face, gives 



TEXTILE CALCULATIONS 66 

28 inches of cloth. Showing a take-up of 11.16 per cent. 31J - 
28 = 31. 31- -f- 28 = .UK) or 11.16 per cent 

These examples could be multiplied, showing the various take- 
ups by using weaves of various intersections and yarns of dilferent 
counts, also by varying the number of threads per inch. 

The following rules are on a basis of 5 per cent, and are given 
as approximately correct. 

RuSe 38. For cotton cloth. To find the number of dents 
per inch in reed to produce a given "sley". 

Deduct 1 from the giveu sley and divide by one of the fol- 
lowing numbers: 

For 1 thread in dent divide by 1.05 
" 2 threads" " " " 2.1 

u 3 u u u u ;; 3^5 

K ^ u a a a a ^2 

Rule 39. To find sley of cloth woven with a reed, the num- 
ber of dents per inch being given. 

Multiply the number of dents per inch by one of the fol~ 
lowino; numbers and add 1: 

For 1 thread in dent multiply by 1.05 

2.10 
3.15 
4.2 

Examples. Find the number of dents per inch in reed, to give 
a 120 sley drawing 4 threads in each dent. 120 - 1 = 119. 119 
~ 4.2 = 28J dents per inch. 

What sley cloth would be woven with a reed containing 50 
dents per inch, with 3 threads in each dent? 50 dents X 3.15 = 
157.5. 157.5 + 1 = 158.5 sley cloth, or threads per inch. 

Rule 40. To find sley reed to produce unequally reeded pat- 
terns such as lenos, cords, dimities, etc. Multiply the threads in 
the pattern by patterns per inch, which will give the average sley: 
then multiply the average sley by the number of dents per pattern 
and by 2, and divide by the number of threads per pattern. 

In a sample of cloth, the pattern is found to be reeded 2, 4, 4, 
4, and there are 9 patterns per inch. What reed will produce it ? 

2-f4 + 4-h4=14 threads in pattern. 14 X 9 = 126 
average sley. 



a 


2 


a 


u 


a 


^i 


'i 


a 


3 


a 


u 


a 


a 


a 


a 


4- 


a 


u 


a 


u 


a 



66 TEXTILE CALCULATIONS 



126 X 4 X 2 



= 72 sley reed. 



14 

72 -^ 2 = 36 actual reed 

AVhen fiffurinor cotton fabrics, allowances must Ue niude for 
quantity of size, starch, and other sul)stances used. 

Worsted Cloth. Tn the analysis and construction of worsted 
fabrics, that is, those composed of worsted \Varp and worsted filling, 
the same principles are to be observed as in cotton cloths. 

Piece dyed worsted goods usually gain as much in weight in 
the dyeing operation as they lose in the process of scouring, so the 
weight of the cloth from the loom may be taken as net, and the 
calculations based accordingly. 

The width of the warp in the reed depends upon the class of 
goods to be made, the required width ot the finished piece, and the 
structure of the design. In ordinary worsted textures, the shrink- 
age of the cloth from the loom to the finished state, varies from 8 
to 12 per cent. 

A sample of finished cloth contains 80 threads and 80 picks 
per inch. Allow 10 per cent for shrinkage in the width and length. 
Find the width of the warp in the reed, and the number of threads 
and picks per inch with which it must be woven. The cloth is 56 

inches wide finished. 

80 V 00 
100% - 10 = 90% ^ = 72 threads and picks per 

inch in loom. 
Threads (80) X width (56) threads in loom (1,480) ^^^ 

threads per inch (72) 72 ~ ~'^ 

inches. 

The original length and width represented 100%. The shrink- 
age was 10%, so the finished cloth is 90% of the original length 
and width. As there are 80 threads and picks per inch in the 
finished cloth, there must have been a smaller number per inch 
when the length and the width were greater. Therefore, multiply 
the number of threads and picks by the finished width and length 
and divide tlie product by the original length and width. 

To find the width in reed: First find the number of ends in 
the warp by multiplying the finished width by number of threads 
per inch in the finished cloth; then divide the ])roduct by the 
threads per inch in the loom. 



TEXTILE CALCULATIONS 67 



Example. A worsted cloth contains 04 warp and fillintr 
threads. Shrinkage 9%. Finished width 55 inches. Find the 
reed width, and the number of threads and picks with whicli it 
should be woven. 

Fancy worsted cloths are made from yarns dyed in the hank, 
or from yarns where the material has been dyed in the raw state 
or in the worsted top, therefore, the loss in scouring and hnisliino; 
mnst be considered. 

Fulled Woolen Goods. Fabrics which come under this head 
may have a finishing shrinkage of 20% to 35%, and in some cases 
even more. Such goods are said to be "made" in finishing, for 
the cloth as produced by the loom would not be recognized in the 
finished condition. 

AYhen analyzing a small sample of woolen goods, it is very 
important that the shrinkage be accurately found, or the reproduc- 
tion will not be a success. 

Method of finding picks in loom. 

Picks in finished cloth X finished length 

z z r-r := picks lu loom. 

length out or loom ^ 

A finished woolen coating has 71 picks per inch. 63 yards 

of cloth out of loom gives 57 yards finished. 

— = b4 picks in loom. 

Or, a finished woolen suiting has 80 picks per inch, and it has 
had a shrinkage in length in the warp, or number of picks, of 
20%. What was the number of picks in the loom? 

100 - 20 = 80%. 80 X 80% = 64 picks in loom. 

There is a large number of fabrics for heavy clothing, tluit 

are made with a back stitched to the original or face fabric in order 

to gain weight and warmth. When analyzing such fabrics the 

counts and weight of the back cloth yarns are calculated as a 

separate cloth. 

CONSTANTS. 

Constants for the customary width of any fabric, whereby the 

weight per yard may be easily obtained from a small sample. 

Formula. 

Width X inches in 1 yard X ounces in 1 lb. 



Grains in 1 lb. (Avoirdupois/ 



constant. 



(38 TEXTILE CALCULATIONS 

54 X 30 X 16 ^ 7,000 = 4.44 constant. 

Rule 41. AVeiglit of sample X the constant -^ scj. in. of 
sample -- weight of yard, given width (54"). 

Sample. 3x2 inches = 24 grains. 

24 X 4.44 _. 



6 


i uzi. uci vaiu.. 


TABLE OF CONSTANTS. 


Inches 


Inches 


wide. 


wide. 


12= .98 


42 = 3.45 


14 = 1.15 


44 = 3.62 


16 = 1.31 


46 = 3.78 


18 = 1.48 


48 = 3.95 


20 = 1.65 


50 = 4.12 


24 = 1.97 


52 = 4.27 


27 = 2.22 


54 = 4.44 


28 = 2.30 


55 = 4.52 


30 = 2.47 


56 = 4.60 


32 = 2.63 


58 = 4.77 


34 = 2.79 


60 = 4.94 


36 = 2.96 


62 = 5.10 


38 = 3.13 


64 = 5.26 


40 = 3.30 


66 = 5.42 



Example. A small sample 1 square inch = 5 grains. What 
is the weight of a yard of cloth 56 inches wide ? 

Constant 4.6 X 5 = 23 ozs. 

The utility of this rule is at once apparent when applied to 
the solution of the above example, or to the following: A given 
sample is 3 X 3 inches and weighs 27 grains. What is the weight 
if the fabric is 28 inches wide? 

27 X 2.3 
3X3 = 9. g = 6.9 ozs. 

EXAMPLES FOR PRACTICE. 

1. A sample is 4 X 1.5 inches and weighs 18.5 grains. 
What will one yard of the fabric w^eigh, 54 inches wide? 

2. What will one yard of cloth, 36 inches wide, w'eigh, if a 
small sample 2J X 2 inches weighs 6.7 grains? 

3. A yard of cloth 40 inches wide weighs 10.3 ozs. What 
will be the weight of a sample 4 X 2| inches? 

4. What will one yard of cloth, 72 inches wide, weigh, if a 
4 X 21-inch sample weighs 30 grains? 



TEXTILE CALCULATIONS 69 



ANALYSIS OF PATTERN. 

Cloths composed of one-color warp and one-color iillincr are 
said to be of solid color, but when there are two or more colors in 
the warp or in the filling, the arrangement of the colors is termed 
the pattern. Where several shades of colors of yarn are used in 
fancy fabrics, to produce certain effects, the order of the threads 
must be carefully noted to make a correct reproduction. Of course 
the order of arrangement of these threads may be ascertained dur- 
ing the process of dissection. 

One thing to be attended to is, that the leading thread in the 
pattern should be found, with reference to the style of the design 
or weave employed. Sometimes particular threads are intended to 
show either prominently or the reverse and a special arrangement in 
the weave is made to produce this result. In such cases the rela- 
tion of the thread to its loorhing arrangement must be strictly 
observed, or the attempt at reproduction will be a failure. If the 
style of weave is all one kind, as in an ordinary twill or sateen 
weave, the above may be disregarded. 

An additional consideration, with regard to these differently 
colored threads in the warp, and one which must receive attention is 
that, whatever number of threads there may be in the pattern, it 
must be repeated an even number of times in the width of the 
warp, so that if the edges of the cloth, minus the selvedges, were 
brought together so as to form a tube, the pattern would be con- 
tinuous all around. 

Suppose that it is necessary to produce a fabric which contains 
16 threads in one repeat of the pattern, as follows: 4 threads 
black, 2 threads drab, 2 threads slate, 4 threads black, 2 threads 
slate, 2 threads drab. This arrangement must be repeated as many 
times as is made necessary by the required width. A few extra 
threads may be disposed of by casting out, or a few may be added 
to make up even patterns. 

Suppose a warp contains 1,920 threads and the pattern is 
composed of 16 threads. 

Threads divided by number of threads in pattern equals num- 
ber of patterns. 1,920 -^ 16 == 120 patterns. 

Suppose a warp fabric is measured and found to be 32^ inches 
wide and there are 48 threads per inch and 16 threads in the pattern. 



70 TEXTIU: ( .\lc:l'lations 



■4S X 32_^ = l.r)4S 111 reads. 
1,548 -f- K) == {)() patterns + 12 threads. 

T/ie 12 e.vfra threads nnist he c<(st out. 

A fabric 35 inches wide contains 2,380 threads in the warp 
and is dressed 2 black, 2 white, 2 black, 1 red. (^a) How many pat- 
terns are there in the warp? (/>) How many threads per inch? 

Relative Weights of Warp and Filling. There is yet an- 
other essential consideration in reference to these varied threads, 
for, in addition to finding the number of each kind, their weight 
also must be obtained, for the purpose of warping and dressing, as 
well as in making out the cost of the fabric. To the designer, 
spinner, and manufacturer calculations of this kind are very useful. 

Find the weight of a warp 64 yards long, made of 2-32's 
worsted, and woven in a 16's reed, 4 threads in a dent, QQ inches 
wide in reed. 

16 X 4 = 64 threads per inch. 2-32's = 16's. 

64" X 66" X 64 (threads per inch) 



16 X 560 



30.1 lbs. 



or 



4,224 64 

threads in the warp X the length o/^ i ^^ 

. _ 1 ^ — ^ ^ = 30.1 lbs. 

counts X standard 

16 560 , 

Example. Find the weight of filling required to weave a 
piece 64 yards long, 64 inches wide in the reed, 80 picks per inch 
of 1-18's worsted. Add 5 per cent to cover the ^yaste in weaving. 
80 X 64" X 64 (yds) X (100 + 5%) 
18 X 560 X 100 = ^*-l ^^'- °* fill'^gy^"- 

It must be remembered that a yard of warp will not weave a 
yard of cloth, and in making calculations, sometimes the length of 
the warp is taken instead of the loom length, the difference in 
lencTth being; considered sufiicient to cover extra cost of waste of 
filling during the weaving. 

EXAMPLES FOR PRACTICE. 

1. Find the weight of warp and filling required to weave a 
piece 63 yards long, 64 inches in the reed, made from 70 yards of 
warp and containing 84 picks per inch, plus 5% for extra filling 
to cover the waste in weaving. Yarn is all 16's worsted. 



TEXTILE CALCULATIONS 71 

2. A fabric 72 yards long is 56 inches wide in the reed, and 
contains 80 picks per inch. Waste in weaving 5%. 80 yards of 
warp are used in the fabric. Find the weight of warp and filling 
if both are 2-4:0's worsted. 

3. 6-1: yards of warp are woven into a fabric 56 yards long. 
In the loom the cloth is 64: inches wdde, and contains 50 picks per 
inch. 5% waste in weaving in filling. Find the weight of warp 
and fillincr if both are IJi's cotton. 

4. A woolen fabric is set 56 inches wide in the reed, and is 
woven with 40 picks per inch; 72 yards of warp finish to 64 yards 
of cloth. 5% waste in filling. What is the weight of warp and 
filling if both are 3-run woolen ? 

5. A 2-48's worsted warp 65 yards long is w^arped to the fol- 
lowing pattern: Woven in a 12 reed, 4 threads in a dent, 60 
inches wide. 

2 black ) 

2 dk brown \ X ^ 

2 dk. brown ) 
2 dk. drab \ X ^ 
24 threads in pattern. 

12 X 4 =- 48. 48 X 60 = 2,880 ends in warp. 
2,880 -^ 24 = 120 patterns. 
Find the weight of each color of yarn. • 
The followinor is the most convenient form to write out the 

o 

scheme of warp and filling, as the summary of the threads can be 
obtained more easily. It is very essential to ascertain he weight, 
of each color and sort of material used, especially in the warp 
where the number of threads of each color and sort must be known, 
so that the several calculations can be made for spooling and warping. 

Black 2 2 2 2 =8 threads. 

Dk. brown 2 2 2 4 2 = 12 " 

Dk. drab 2 2 = 4 " 

24 "in pattern. 

120 patterns X 8 threads = 960 Black. 
120 " X 12 " = 1,440 Dk. brown. 
120 " X 4 " = 480 Dk. drab, 

■pso 



72 TEXTILE CALCULATIONS 

The weight of each kind can now be obtained by the regular 

method. 

960 X 65 
24"X "560- = ^-^^^ ^^^• 



1,440 X 65 
24 X 560 

480 X 65 
24 X 560 



= 6.96 lbs. 
= 2.32 lbs. 



13.92 total weight of warp. 
There is another method of obtaining the number of threads 
of each color. 

Total number of warp threads X threads of any color in one repeat 
Number of threads in pattern. 

24 " ^'^*^- 

In patterns where there is a large number of threads of one 
color, as may be the case in a Scotch or Tartan plaid, it is advis- 
able to commence the color scheme by dividing the largest number 
of threads, coinmencing with one-half and ending with the other. 

A plaid is made from 2-24's worsted w^arp and filling, 12's 
reed, 4 in one dent, 44 picks per inch, width within selvedges 36 
inches, plus 24 threads on each side for selvedges. The warp 
take-up is 15% during weaving, 60 yds. of warp before weaving. 
Selvedges, white 2-24's worsted. 

Black 24 6 20 20 6 24 == 100 

White 12 6 68 6 12 =- 104 

Ked 6 6 =12 

2l6 
This pattern has purposely been started with 24 threads of 
black (note the selvedges are white), and finished with the same 
number and color. If the selvedges had been ordered black, the 
pattern would have commenced with 34 white. 

48 X 36 = 1,728. 1,728 ^ 216 = 8 repeats. 
Black 100 X 8 == 800 X 60 ^ (12 X 560) = 7.14 lbs. 
White 104 X 8 = 832 X 60 
Eed 12 X 8 = 96 X 60 

iV728 15.43 lbs. 

Selvedges white 48 X 60 -:- (12 X 560) =^ .43 lbs. 

T5:86 

Note.— "The selvedge may be added to white in body of warp. 



(12 X 560) = 7.43 lbs. 
(12 X 560) = .86 lbs. 



TEXTILE CALCULATIONS 78 

The weight of each color of filling is obtained by the use of a 
similar formula, but the width includes the selvedgeSo 
36 + 1 = 37" X 44 pks. = 1,628. 
1,628 ^ 216 = 7.54. 
Black 7.54 X 100 = 754 
White 7.54 X 104 =^ 784 
Red 7.54 X 12 = 90 

i;628" 
37 X 44 X 60 ^^ ^ ^^ ^ . , ^^^^. 

— 1.) w rpo = 14.^ lbs., total weight of nlling. 

14.5 X 100 „_,, ,^, , ,.„. 
^jo = b.rZ lbs. of black nlling. 

14.5 X 104 

— — 6.98 lbs. of white filling- 

14.5 X 104 

— — =: .80 lbs. or red nlling. 

14.5 total weight of filling. 

The total weight can first be obtained, and then the proportions 
of weight of each color may be determined by the ratio of picks of 
each color to the total number of picks in each repeat, or multiply 
the number of picks per inch by 36, to find the number of picks 
in one yard, then multiply the result by the length of the warp, 
which will give the total number of picks in the whole piece. 
Divide the total number of picks by the number of picks in the 
pattern, to find the number of repeats. Multiply the repeats by 
the number of picks of each kind of filling, and again multiply 
these products by the width of the warp in the reed in the loom, 
which will give the total number of inches of filling of each kind. 
Divide the results by 36 to reduce to yards and by the counts of 
the yarn multiplied by the standard number to obtain the weight. 

Lay a warp 72 inches wide in loom, 60 yards long, 4-run 
yarn. (40 picks per inch.) 



of filling. 


20 picks black 




1 '' brown 




6 " black 




1 " brown 




20 " black 




48 



74 TEXTILE CALCULATIONS 



There are 46 picks of black and 2 picks of brown in the pat- 
tern. Find the amount of yarn required of each color. 

36" 
40 picks per inch 
1,440 " " yard 
60 



86,400 picks in 60 yards 

Total number of picks (86,400) 

Pi,k3 i,, pattern (48 ) == ^'^^^ ^^P^^^^' 

Brown 1,800 X 2 X 72 ^ ^^^ 

gg = 7,200 yards. 

7,200 

— — — =z 18 ounces. 

Black 1,800 X 46 X 72 

o7! = 1oo,dOO yards. 

165,600 

— 7777^^ — = 414 ounces. - 
400 

The same rule applies to the picks of worsted and cotton by 
using their respective counts and standard numbers. 



EXAMINATION PAPER 



TEXTILE CALCULATIONS 



Read carefully : Place your name and full address at the head of the 
paper. Any cheap, light paper like the sample previously seutyou may be 
used. Do not crowd j^ourwork, but arrange it neatly and legibly. Do not 
copy the ansicei'S from the Instruction Paper; use your oivn ivords, so that 
ice may be sure that you understand the subject. 



1. Find the worsted counts of tlie following yarns: 10,080 
yards weigh 1 lb.; 9,240 yards weigh 12 ozs; 17,500 yards 
weigh 1^ lbs. 

2. Find the woolen runs of the following yarns: 6,400 
yards weigh 1 lb.; 2,100 yards weigh 4 ounces; 8,400 yards weigh 
51 lbs. 

3. Find the cotton counts of the following yarns: 33,600 
yards weigh 1 lb.; 20,160 yards weigh fib.; 100,800 yards 
weigh 1^ lbs. 

4. What is the weight of 21,840 yards of 13's worsted yarn ? 
31,500 yards of 15's cotton yarn? 4,800 yards of 6-run woolen 
yarn? and 134,400 yards of 20's spun silk? 

5. Change the following yarns to cotton counts: 60's worsted; 
10-run woolen; and 14-lea linen. 

6. Change the following yarns to w^orsted counts: 16's cot- 
ton; 7-run woolen; and 24's spun silk. 

7. Give the metric counts of the following yarns: 28's 
worsted; 5-run woolen; and 32's cotton. 

8. Give the counts of the compound threads when the fol- 
lowing yarns are twisted together: 36's and 30's worsted; 120's 
and 60's cotton; 30's and 60's spun silk. 

9. Find the counts of a 3-ply thread composed of 60's, 30's, 
and 15's worsted; 72's, 36's, and 24's cotton; 12-run, 6-run, and 
4- run woolen. 

10. What is the counts of a novelty yarn composed of one 
thread each of 60's, 48's, and 36's cotton? The relative lengths of 
yarn used are 5, 4, and 2 inches. The 36's thread of which 2 
inches are used is straight or 100%. 



TEXTILE CALCULATIONS 



11. If a mill has 600 lbs. of 24'8 worsted, what weight of 18's 
worsted will be required to twist with it to work it all up, and what 
is the counts of the compound thread? 

12. Find the average counts in a pattern composed of 4 threads 
of ()0's cotton, 2 threads of^48's cotton and 1 thread of 30's cotton. 

13. Find the diameters of the following yarns: 32's worsted, 
lOO's cotton, and 8 -run woolen. 

14. How many threads of each of the yarns in Problem 13 
will lie side by side in a cloth woven with the plain weave? 

15. A sample of worsted cloth contains 60 threads, and 60 
picks per inch. Allow 5% for shrinkage in width and length and 
find the number of threads and picks per inch with which the 
cloth was woven. 

16-20. Analysis of Worsted Trousering. 

Data. One square inch = 3.5 grains. 

Width within selvedges, 28 inches. 

68 threads per inch = 1.9 grains. 

64 picks per inch =^ 1.6 grains. 

Warp pattern; 3 slate; 2 black; 2 mix; 1 black = 8 threads. 

Fillinor; solid black. 

Find the following particulars: 

(a) Weight of one yard inside selvedges. 

(h) Threads in the warp. 

(c) Patterns in the warp. 

(d) Counts of warp in finished cloth, 

(e) Counts of filling in finished cloth. 

(/') Weight of warp yarn in one yard of finished cloth. 

(g) Weight of filling yarn in one yard of finished cloth. 

After completing the work, add and sign the following statement: 

I hereby certify that the above work is entirely my own. 

(Signed) 



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i.U. 23^t'Jt 



